Kripke bundle [3] and C-set semantics [1] [2] are known as semantics which generalize standard Kripke semantics. In [3] and in [1], [2] it is shown that Kripke bundle and C-set semantics are stronger than standard Kripke semantics. Also it is true that C-set semantics for superintuitionistic logics is stronger than Kripke bundle semantics [5].In this paper, we show that Q-S4.1 is not Kripke bundle complete via C-set models. As a corollary we can (...) give a simple proof showing that C-set semantics for modal logics are stronger than Kripke bundle semantics. (shrink)

This investigation examined whether speakers produce reliable prosodic correlates to meaning across semantic domains and whether listeners use these cues to derive word meaning from novel words. Speakers were asked to produce phrases in infant‐directed speech in which novel words were used to convey one of two meanings from a set of antonym pairs (e.g., big/small). Acoustic analyses revealed that some acoustic features were correlated with overall valence of the meaning. However, each word meaning also displayed a unique acoustic signature, (...) and semantically related meanings elicited similar acoustic profiles. In two perceptual tests, listeners either attempted to identify the novel words with a matching meaning dimension (picture pair) or with mismatched meaning dimensions. Listeners inferred the meaning of the novel words significantly more often when prosody matched the word meaning choices than when prosody mismatched. These findings suggest that speech contains reliable prosodic markers to word meaning and that listeners use these prosodic cues to differentiate meanings. That prosody is semantic suggests a reconceptualization of traditional distinctions between linguistic and nonlinguistic properties of spoken language. (shrink)

An advanced introduction to semantics that presents this crucial component of human language through the lens of the 'Meaning-Text' theory - an approach that treats linguistic knowledge as a huge inventory of correspondences between thought and speech. Formally, semantics is viewed as an organized set of rules that connect a representation of meaning (Semantic Representation) to a representation of the sentence (Deep-Syntactic Representation).

The comprehension principle of set theory asserts that a set can be formed from the objects satisfying any given property. The principle leads to immediate contradictions if it is formalized as an axiom scheme within classical first order logic. A resolution of the set paradoxes results if the principle is formalized instead as two rules of deduction in a natural deduction presentation of logic. This presentation of the comprehension principle for sets as semantic rules, instead of as a comprehension axiom (...) scheme, can be viewed as an extension of classical logic, in contrast to the assertion of extra-logical axioms expressing truths about a pre-existing or constructed universe of sets. The paradoxes are disarmed in the extended classical semantics because truth values are only assigned to those sentences that can be grounded in atomic sentences. (shrink)

This study examines BDI logics in the context of Gabbay's fibring semantics. We show that dovetailing can be adopted as a semantic methodology to combine BDI logics. We develop a set of interaction axioms that can capture static as well as dynamic aspects of the mental states in BDI systems, using Catach's incestual schema G^[a, b, c, d]. Further we exemplify the constraints required on fibring function to capture the semantics of interactions among modalities. The advantages of having (...) a fibred approach is discussed in the final section. (shrink)

In recent papers Hans Halvorson has offered a critique of the semantic view of theories, showing that theories may be the same although the corresponding sets of models are different and, conversely, that theories may be different although the corresponding sets of models are the same. This critique will be assessed, first, as it pertains to issues concerning scientific models in the empirical sciences and, second, independent of any concern with empirical science.

I argue that the medieval form of dialectical disputation known as obligationes can be viewed as a logical game of consistency maintenance. The game has two participants, Opponent and Respondent. Opponent puts forward a proposition P; Respondent must concede, deny or doubt, on the basis of inferential relations between P and previously accepted or denied propositions, or, in case there is none, on the basis of the common set of beliefs. Respondent loses the game if he concedes a contradictory set (...) of propositions. Opponent loses the game if Respondent is able to maintain consistency during the stipulated period of time. The obligational rules are here formalised by means of familiar notational devices, and the application of some game-theoretical concepts, such as (winning) strategy, moves, motivation, allows for an analysis of some crucial properties of the game. In particular, the primacy of inferential (syntactic) relations over semantic aspects and the dynamic character of obligations are outlined. (shrink)

'Mass terms', words like water, rice and traffic, have proved very difficult to accommodate in any theory of meaning since, unlike count nouns such as house or dog, they cannot be viewed as part of a logical set and differ in their grammatical properties. In this study, motivated by the need to design a computer program for understanding natural language utterances incorporating mass terms, Harry Bunt provides a thorough analysis of the problem and offers an original and detailed solution. An (...) extension of classical set theory, Ensemble Theory, is defined, and this provides the conceptual basis of a framework for the analysis of natural language meaning which Dr Bunt calls Two-level model-theoretic semantics. The validity of the framework is convincingly demonstrated by the formal analysis of a fragment of English including sentences with quantified and modified mass terms. Separate chapters of the book are devoted to an axiomatic definition of Ensemble Theory and a detailed discussion of its status as a mathematical formalism. (shrink)

Kripke bundle and C-set semantics are known as semantics which generalize standard Kripke semantics. In [4] and in [1, 2] it is shown that Kripke bundle and C-set semantics are stronger than standard Kripke semantics. Also it is true that C-set semantics for superintuitionistic logics is stronger than Kripke bundle semantics . Modal predicate logic Q-S4.1 is not Kripke bundle complete of the present paper). This is shown by using difference of Kripke bundle (...) semantics and C-set semantics. In this paper, by using the same idea we show that incompleteness results in Kripke bundle semantics which are extended versions of [2]. (shrink)

Regular polysemes are sets of ambiguous words that all share the same relationship between their meanings, such as CHICKEN and LOBSTER both referring to an animal or its meat. To probe how a distributional semantic model, here exemplified by bidirectional encoder representations from transformers (BERT), represents regular polysemy, we analyzed whether its embeddings support answering sense analogy questions similar to “is the mapping between CHICKEN (as an animal) and CHICKEN (as a meat) similar to that which maps between LOBSTER (as (...) an animal) to LOBSTER (as a meat)?” We did so using the LRcos model, which combines a logistic regression classifier of different categories (e.g., animal vs. meat) with a measure of cosine similarity. We found that (a) the model was sensitive to the shared structure within a given regular relationship; (b) the shared structure varies across different regular relationships (e.g., animal/meat vs. location/organization), potentially reflective of a “regularity continuum;” (c) some high-order latent structure is shared across different regular relationships, suggestive of a similar latent structure across different types of relationships; and (d) there is a lack of evidence for the aforementioned effects being explained by meaning overlap. Lastly, we found that both components of the LRcos model made important contributions to accurate responding and that a variation of this method could yield an accuracy boost of 10% in answering sense analogy questions. These findings enrich previous theoretical work on regular polysemy with a computationally explicit theory and methods, and provide evidence for an important organizational principle for the mental lexicon and the broader conceptual knowledge system. (shrink)

In Concepts, Kinds, and Cognitive Development, Frank C. Keil provides a coherent account of how concepts and word meanings develop in children, adding to our understanding of the representational nature of concepts and word meanings at all ages. Keil argues that it is impossible to adequately understand the nature of conceptual representation without also considering the issue of learning. Weaving together issues in cognitive development, philosophy, and cognitive psychology, he reconciles numerous theories, backed by empirical evidence from nominal kinds studies, (...) natural-kinds studies, and studies of fundamental categorical distinctions. He shows that all this evidence, when put together, leads to a better understanding of semantic and conceptual development. The book opens with an analysis of the problems of modeling qualitative changes in conceptual development, investigating how concepts of natural kinds, nominal kinds, and artifacts evolve. The studies on nominal kinds document a powerful and unambiguous developmental pattern indicating a shift from a reliance on global tabulations of characteristic features to what appears to be a small set of defining ones. The studies on natural kinds document an analogous shift toward a core theory instead of simple definition. Both sets of studies are strongly supported by cross cultural data. While these patterns seem to suggest that the young child organizes concepts according to characteristic features, Keil argues that there is a framework of conceptual categories and causal beliefs that enables even very young children to understand kinds at a deeper, theoretically guided, level. This account suggests a new way of understanding qualitative change and carries strong implications for how concepts are represented at any point in development. A Bradford Book. (shrink)

Lexical ambiguity—the phenomenon of a single word having multiple, distinguishable senses—is pervasive in language. Both the degree of ambiguity of a word (roughly, its number of senses) and the relatedness of those senses have been found to have widespread effects on language acquisition and processing. Recently, distributional approaches to semantics, in which a word's meaning is determined by its contexts, have led to successful research quantifying the degree of ambiguity, but these measures have not distinguished between the ambiguity of (...) words with multiple related senses versus multiple unrelated meanings. In this work, we present the first assessment of whether distributional meaning representations can capture the ambiguity structure of a word, including both the number and relatedness of senses. On a very large sample of English words, we find that some, but not all, distributional semantic representations that we test exhibit detectable differences between sets of monosemes (unambiguous words; N = 964), polysemes (with multiple related senses; N = 4,096), and homonyms (with multiple unrelated senses; N = 355). Our findings begin to answer open questions from earlier work regarding whether distributional semantic representations of words, which successfully capture various semantic relationships, also reflect fine‐grained aspects of meaning structure that influence human behavior. Our findings emphasize the importance of measuring whether proposed lexical representations capture such distinctions: In addition to standard benchmarks that test the similarity structure of distributional semantic models, we need to also consider whether they have cognitively plausible ambiguity structure. (shrink)

“The object of this book,” writes William C. Dowling in his preface, “is to make the key concepts of Paul Ricoeur’s _Time and Narrative_ available to readers who might have felt bewildered by the twists and turns of its argument.” The sources of puzzlement are, he notes, many. For some, it is Ricoeur’s famously indirect style of presentation, in which the polarities of argument and exegesis seem so often and so suddenly to have reversed themselves. For others, it is the (...) extraordinary intellectual range of Ricoeur’s argument, drawing on traditions as distant from each other as Heideggerian existentialism, French structuralism, and Anglo-American analytic philosophy. Yet beneath the labyrinthian surface of Ricoeur’s _Temps et récit_, Dowling reveals a single extended argument that, though developed unsystematically, is meant to be understood in systematic terms. __Ricoeur on Time and Narrative_ _presents that argument in clear and concise terms, in a way that will be enlightening both to readers new to Ricoeur and those who may have felt themselves adrift in the complexities of _Temps et récit,_ Ricoeur’s last major philosophical work. Dowling divides his discussion into six chapters, all closely involved with specific arguments in _Temps et récit_: on mimesis, time, narrativity, semantics of action, poetics of history, and poetics of fiction. Additionally, Dowling provides a preface that lays out the French intellectual context of Ricoeur's philosophical method. An appendix presents his English translation of a personal interview in which Ricoeur, having completed _Time and Narrative, _looks back over his long career as an internationally renowned philosopher. __Ricoeur on Time and Narrative___ _communicates to readers the intellectual excitement of following Ricoeur’s dismantling of established theories and arguments—Aristotle and Augustine and Husserl on time, Frye and Greimas on narrative structure, Arthur Danto and Louis O. Mink on the nature of historical explanation—while coming to see how, under the pressure of Ricoeur’s analysis, these ideas are reconstituted and revealed in a new set of relations to one another. "The scholarship in William C. Dowling's __Ricoeur on Time and Narrative____ __is impeccable; Dowling knows Ricoeur inside out. He highlights Ricoeur's most important arguments, presents them in a limpid, concise language, and links them to the relevant nineteenth- and twentieth-century philosophical developments. Dowling's book provides us with a lucid, intelligible version of Ricoeur's major work, one that will be of considerable significance to philosophers, historians, and literary theorists." —_Thomas Pavel, Gordon J. Laing Distinguished Service Professor of French Literature, and the Committee on Social Thought, University of Chicago_ "William C. Dowling's __Ricoeur on Time and Narrative___ _is a subtle and remarkably well-sustained piece of work. It provides a detailed introduction to a major work of philosophy and narrative theory—already a considerable achievement, given the difficulty of Ricoeur's text. However, Dowling also shows us, sometimes explicitly, sometimes simply through the way he conducts his argument, why we should bother with Ricoeur—what we have to gain from knowing him better than we do, however well we may think we know him." —_Michael Wood, Charles Barnwell Straut Class of 1923 Professor of English and Comparative Literature, Princeton University _. (shrink)

The semantics of anaphoric pronouns or _relativa grammaticalia_ played an important role in the treatises of both grammarians and logicians in the middle ages. However only very recently has the theme again received comparable attention in transformational grammar and the analytic school of linguistic philosophy under the influence of Geach. Here philosophers of language take particular interest in the question of how far these expressions can be seen as colloquial counterparts of the bound variables known from predicate logic. This (...) work shows that scholastic theories of _suppositio relativorum_ underwent a development in the 14th century and that the theories which gradually emerged anticipated in important ways the insights of recent linguistic philosophy. This thesis is illustrated by editions of selected texts of the logicians of the new continental universities of Vienna and Prague of the end of the 14th and the beginning of the 15th centuries and make it clear that the often asserted decline of scholasticism had not yet set in in the period after Ockham and Buridan. (shrink)

Mitchell, J.C. and E. Moggi, Kripke-style models for typed lambda calculus, Annals of Pure and Applied Logic 51 99–124. The semantics of typed lambda calculus is usually described using Henkin models, consisting of functions over some collection of sets, or concrete cartesian closed categories, which are essentially equivalent. We describe a more general class of Kripke-style models. In categorical terms, our Kripke lambda models are cartesian closed subcategories of the presheaves over a poset. To those familiar with Kripke models (...) of modal or intuitionistic logics, Kripke lambda models are likely to seem adequately ‘semantic’. However, when viewed as cartesian closed categories, they do not have the property variously referred to as concreteness, well- pointedness or having enough points. While the traditional lambda calculus proof system is not complete for Henkin models that may have empty types, we prove strong completeness for Kripke models. In fact, every set of equations that is closed under implication is the theory of a single Kripke model. We also develop some properties of logical relations over Kripke structures, showing that every theory is the theory of a model determined by a Kripke equivalence relation over a Henkin model. We discuss cartesian closed categories but present the main definitions and results without the use of category theory. (shrink)

This volume began as a remembrance of Alonzo Church while he was still with us and is now finally complete. It contains papers by many well-known scholars, most of whom have been directly influenced by Church's own work. Often the emphasis is on foundational issues in logic, mathematics, computation, and philosophy - as was the case with Church's contributions, now universally recognized as having been of profound fundamental significance in those areas. The volume will be of interest to logicians, computer (...) scientists, philosophers, and linguists. The contributions concern classical first-order logic, higher-order logic, non-classical theories of implication, set theories with universal sets, the logical and semantical paradoxes, the lambda-calculus, especially as it is used in computation, philosophical issues about meaning and ontology in the abstract sciences and in natural language, and much else. The material will be accessible to specialists in these areas and to advanced graduate students in the respective fields. (shrink)

In his pioneering work in the field of inductive inference, Gold (Inf Control 10:447–474, 1967) proved that a set containing all finite languages and at least one infinite language over the same fixed alphabet is not identifiable in the limit (learnable in the exact sense) from complete texts. Gold’s work paved the way for computational learning theories of language and has implications for two linguistically relevant classes in the Chomsky hierarchy (cf. Chomsky in Inf Control 2:137–167, 1959, Chomsky in Knowledge (...) of language: its nature, origin, and use, Praeger, 1986; Shieber in Linguist Philos 8:333–343, 1985; Heinz in Linguist Inq 41:623–661, 2010). Within that same framework, Angluin (Inf Control 45:117–135, 1980) provided a complete characterization for the learnability of language families. Mathematically, the concept of identification in the limit from that classical setting can be seen as the use of a particular type of metric for learning in the limit (Wharton in Inf Control 26:236–255, 1974). In this research note, I use Niyogi’s extended version of a theorem by Blum and Blum (Inf Control 28:125–155, 1975) on the existence of locking data sets to prove a necessary condition for learnability in the limit of any family of languages with the Gold property in any given metric. This recovers the most general version of Gold’s Theorem as a particular case. Moreover, when the language family is further assumed to contain all finite languages, the same condition also becomes sufficient for learnability in the limit. Finally, we discuss questions that are left open and outline a research program regarding language learnability in the limit from other input types and cognitive feasibility. (shrink)

This anthology consists of forty-nine of Geach’s previously published papers on logic. He opens his Preface by writing: "I bring together here almost all my English articles that I have previously published and have not already collected or cannibalized in other books." It contains his first published paper "Designation and Truth" from Analysis 1947-48 as well as his elegant sketch of a decidable entailment system in the 1970 Philosophical Review. For the most part he has made only stylistic changes and (...) added some notes. So, he claims: "all articles appear without substantial change." However, he admits that he divided his "Quantification Theory and the Problem of Identifying Objects of Reference" from the now classic 1963 volume of Acta Philosophica Fennica. He divided it because he wanted to separate his strong advocacy of a substitution interpretation of the quantifiers from some views on quotation marks, about which he is less than certain. The papers are not in mere chronological order. They are organized by topic within chapters entitled: Historical Essays, Traditional Logic, Theory of Reference and Syntax, Intentionality, Quotation and Semantics, Set Theory, Identity Theory, Assertion, Imperatives and Practical Reasoning, and Logic in Metaphysics and Theology. The chapter titles are a fair guide to content. But note the following. Two lucid papers defending von Wright’s notion of entailment are in the Intentionality chapter. The essay "Ascriptivism" in the Assertion chapter is relevant to discussions of free will because he argues: "to ascribe an act to agent is a causal description of the act" and he urges a search for a non-Humean analysis of causality. The essays in the last chapter are: "Nominalism," "Some problems about time," and "God’s relation to the world.". (shrink)

The Chinese room thought experiment of John Searle militates against strong artificial intelligence, illustrating his claim that syntactical knowledge by itself is neither constitutive nor sufficient for semantic understanding as found in human minds. This thought experiment was put to a behavioural test, concerning the syntax of a finite algebraic field. Input, rules and output were presented with letters instead of numbers. The set of rules was first presented as a table but finally internalized by the participants. Quite in line (...) with Searle's argument, uninformed participants mastered the syntax but did not explicitly report semantic knowledge. In order to test the virtual mind reply to the Chinese room argument, the reaction time pattern of the participants was compared to that of an informed control group. The correlation was quite high but could be traced back to memory load and response priming, i.e. to syntactical factors. No trace of tacit semantic knowledge of the task could be found in the experimental group. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Philosophy of Peter Abelard by John MarenbonConstant MewsJohn Marenbon. The Philosophy of Peter Abelard. Cambridge: Cambridge University Press, 1997. Pp. xx + 373. Cloth, £40.Peter Abelard (1079–1142) has long provoked conflicting responses from readers. Even in his own lifetime opinions varied from the adulation of loyal disciples to a chorus of hostility from St. Bernard and others. Inevitably these debates have colored subsequent perception of Abelard’s achievement. (...) It was only through the pioneering efforts of Victor Cousin that Abelard’s writings on logic, as distinct from those on theology and scriptural exegesis, first began to see the light of day. As John Marenbon documents in a fascinating appendix to a magisterial volume, Cousin’s emphasis on Abelard as a dialectician tended to reinforce existing stereotypes about him as a critical rather than as a constructive thinker.Marenbon sets out to counter such perceptions. His book is structured in three separate sections: a historical survey of Abelard’s life and writings on logic and theology; [End Page 621] an analysis of his ideas on substance, language, epistemology and universals; and a study of the ethical foundations of his thought. This tripartite structure shapes his analysis in profound ways. The initial section has the merit of synthesizing recent research (including my own) about our understanding of the chronological evolution of Abelard’s writings with lucidity and perspicacity. The real originality of this book, however, emerges in its second section with the chapter ‘Logic, philosophy and exegesis.’ Here Marenbon presents a succinct account of the ontological framework inherited by Abelard through Aristotle’s Categories and Porphyry’s introduction to it, the Isagoge, as well as Abelard’s response to it. Marenbon’s comment (109) that nominalists did not think that there was no thing which was not a particular, but instead expounded the Isagoge and Categories as having to do with words rather than things sets the tone for his analysis of Abelard’s ontology, presented as being much more subtle than a naive rejection of universal things. His thesis is that this ontology combines three separate principles: nominalism, ‘strong naturalism’ (defined as Aristotle’s belief that every member of a given natural kind has the same basic structure of genera, species and differentiae), and a strict view of the separateness of particular things.To a modern eye, these principles might seem to be mutually exclusive. Marenbon shows how Abelard constructs an ontology taking its point of departure from the particularity of things, and so transforms Porphyry’s hierarchy of being into one which is based on individuals. Unlike earlier scholars, (notably Jean Jolivet, author of a brilliant study of Abelard’s semantics and its implications for theology), Marenbon is able to profit from a far deeper awareness of the evolution of Abelard’s thinking about specific logical problems. He is thus able to describe, sometimes in minute detail, how Abelard wrestled with intellectual inconsistencies inherited from the differing strands in his own tradition. Thus he shows how, after the Dialectica and early glosses on Porphyry and Aristotle, Abelard moves away from a simplistic semantics of denomination, by which words denote corresponding forms, and starts to interpret certain accidents (like whiteness) as not having a separate reality. This evolution in Abelard’s semantic thought is mainly known only through passages revised in his Christian Theology. Marenbon suggests that Abelard may have been influenced here by transferring ideas about the three divine persons as differing in attribute to the ordinary world.One difficulty with the structure Marenbon has chosen is that the reader sometimes has to keep backtracking in Abelard’s career. Thus while he provides an outstanding exegesis of Abelard’s theory of cognition (making full use of the long neglected De intellectibus), developed in the 1120s, he then backtracks to the issue of universals. The evolution of Abelard’s thinking on this topic is related, however, to that in other domains. While Marenbon avoids historicizing interpretations (having assigned historical analysis to the first part of his book), it does seem that the evolution of Abelard’s thought was influenced by a desire to distance himself from the categories of thought of his various teachers.Marenbon... (shrink)

In this article we wish to present the typographic experimentations of four designers, each of whom looks at typography and its implementations from different viewpoints; however with similar goals – namely to investigate how typographic systems can be implemented, their attributes as carriers of semantic meaning be redefined, and/or their functions be improved upon within the digital medium that presents challenges as well as opportunities that enable graphic designers to reach well beyond the traditional medium of typographic work; i.e., printed (...) paper. The article will examine these four projects under the umbrella concept of Deconstruction, also extending into a consideration of Legibility; setting them forth as examples of the impact that the digital medium has brought to bear upon typographic practice in recent decades. (shrink)

The proposed multilevel framework of discourse comprehension includes the surface code, the textbase, the situation model, the genre and rhetorical structure, and the pragmatic communication level. We describe these five levels when comprehension succeeds and also when there are communication misalignments and comprehension breakdowns. A computer tool has been developed, called Coh-Metrix, that scales discourse (oral or print) on dozens of measures associated with the first four discourse levels. The measurement of these levels with an automated tool helps researchers track (...) and better understand multilevel discourse comprehension. Two sets of analyses illustrate the utility of Coh-Metrix in discourse theory and educational practice. First, Coh-Metrix was used to measure the cohesion of the text base and situation model, as well as potential extraneous variables, in a sample of published studies that manipulated text cohesion. This analysis helped us better understand what was precisely manipulated in these studies and the implications for discourse comprehension mechanisms. Second, Coh-Metrix analyses are reported for samples of narrative and science texts in order to advance the argument that traditional text difficulty measures are limited because they fail to accommodate most of the levels of the multilevel discourse comprehension framework. (shrink)

We investigate the higher-order modal logic , which is a variant of the system presented in our previous work. A semantics for that system, founded on the theory of quasi sets, is outlined. We show how such a semantics, motivated by the very intuitive base of Schrödinger logics, provides an alternative way to formalize some intensional concepts and features which have been used in recent discussions on the logical foundations of quantum mechanics; for example, that some terms like (...) 'electron' have no precise reference and that 'identical' particles cannot be named unambiguously. In the last section, we sketch a classical semantics for quasi set theory. (shrink)

Depending on what one means by the main connective of logic, the -if..., then... -, several systems of logic result: classic and modal logics, intuitionistic logic or relevance logic. This book presents the underlying ideas, the syntax and the semantics of these logics. Soundness and completeness are shown constructively and in a uniform way. Attention is paid to the interdisciplinary role of logic: its embedding in the foundations of mathematics and its intimate connection with philosophy, in particular the philosophy (...) of language. Set theory is presented both as a conditio sine qua non for logic and as a interesting exact ontology. The study of infinite sets yields perplexing results. Formalization of informal number theory results in formal number theory; Godel's incompleteness is treated. At appropriate places attention is paid to paradoxes, intuitionism, conditionals, the historical development of logic, to logic programming and automated theorem proving for classical logic.". (shrink)

A graph-theoretic account of fibring of logics is developed, capitalizing on the interleaving characteristics of fibring at the linguistic, semantic and proof levels. Fibring of two signatures is seen as a multi-graph (m-graph) where the nodes and the m-edges include the sorts and the constructors of the signatures at hand. Fibring of two models is a multi-graph (m-graph) where the nodes and the m-edges are the values and the operations in the models, respectively. Fibring of two deductive systems is an (...) m-graph whose nodes are language expressions and the m-edges represent the inference rules of the two original systems. The sobriety of the approach is confirmed by proving that all the fibring notions are universal constructions. This graph-theoretic view is general enough to accommodate very different fibrings of propositional based logics encompassing logics with non-deterministic semantics, logics with an algebraic semantics, logics with partial semantics and substructural logics, among others. Soundness and weak completeness are proved to be preserved under very general conditions. Strong completeness is also shown to be preserved under tighter conditions. In this setting, the collapsing problem appearing in several combinations of logic systems can be avoided. (shrink)

Languages play an essential role in communicating aesthetic, scientific and religious convictions, as well as laws, worldviews and truths. Additionally, metaphors are an essential part of many languages and artistic expressions. In this paper I will first examine the role metaphors play in religion and art. Is there a specific focus on symbolic and metaphoric language in religion and art? Where are the analogies to be found in artistic metaphors and religious ones? How are differences to be described? How do (...) various concepts of aesthetics and theological concepts explain those different kinds of language and how, if at all, do they make use of them? Lastly: what could be added to aesthetics, philosophy and theology by examining carefully the role and importance of language, including nonverbal, sign language and especially metaphorical language? Without the human capacity for language, religions are scarcely imaginable. A widening of traditional exegesis and hermeneutics by taking into account nonverbal semantics is needed. Religion is a cognitive and linguistic phenomenon. By taking this seriously, we set and enable an agenda to discuss religion scientifically, leaving aside for the purpose of a scientific understanding and discourse about the inter-religious and the inner-religious claims of truth and absolutist claims. To sum it up: metaphor is introduced as an important means of language when it comes to religious conceptualization. Next, I will show that art, more than religion, deals with visual metaphor – the latter being an image that suggests a particular association, similarity or analogy between two generally unconnected visual elements. This often, but not always, functions in a roughly comparable fashion to the better-known concept of verbal metaphor. In addition, visual metaphor has developed many original and unique characteristics. These two sections are followed by another one dealing with cultural philosophy of religion and aesthetics, as well as the meaning of metaphors for these disciplines. The next section is on metaphor and metaphorical language in mathematics, natural sciences and art and how they are related, i.e. influence and help each other. I will discuss the critical approach to metaphors in natural science and provide a short introduction to the cultural history of mathematics and art. Mathematicians and artists have long been on the quest to understand the physical world they see before them and the abstract objects they know by thought alone. How have art and mathematics helped each other in representing each other’s concepts? A final section provides a summary and an outlook: theology is contextual as is science – and so is art. All these disciplines partly rely upon metaphor and by the help of metaphor get closer to an intercultural and interdisciplinary understanding. I shall argue that, by dealing more carefully with their metaphorical language and their own metaphors, together they become better equipped to map the world. (shrink)

Plural pronouns create the possibility of overlapping reference, which does not not fit naturally into the classical GB theory of anaphora, where each NP has a single integer as its referential index. Thus, one must either complicate the indexing system used in syntax or complicate the semantic interpretation of indices. This paper argues for the former approach based on the properties of a particular comitative-like construction found in Mohawk and certain other languages. This construction is analyzed as a type of (...) Left Dislocation where the dislocated NP forms a syntactic chain with a pronoun that it overlaps in reference with. Several unusual characteristics of such chains can be accounted for if plural pronouns have sets of integers as their indices—characteristics involving bound anaphora, ellipsis interpretation, and connectivity effects. Certain implications for the theory of chains are also discussed. (shrink)

This volume is an offshoot of a symposium on the relation between philology and philosophy that occurred at the 1980 Eastern Division Meeting of the American Philosophical Association, jointly sponsored by the Committee on International Cooperation and the Thyssen Stiftung. It consists of nine papers that explore the linguistic, philological, cultural, and philosophical problems associated with translating Kant's texts into English. As a whole, the volume attempts to provide a unified framework within which future Kant scholarship and interpretation can proceed (...) without falling prey to the mistakes of the past, and its general thesis is that if future translation is to achieve semantic equivalence, the translator must engage in careful exegesis in the context of an appreciation of eighteenth-century philosophical usage and its roots in German school-philosophy, and most important of all, must have a philosophical understanding of Kant's critical philosophy. According to Gram, this collection presents a unique contribution in being "the first useful attempt to explore this area" and the resolution of the problems it poses "constitutes a set of conditions for the possibility of any future translation of Kant's work"--an obvious echoing of the full title of one of Kant's most well-known works. (shrink)

This paper studies a family of monotonic extensions of first-order logic which we call modulated logics, constructed by extending classical logic through generalized quantifiers called modulated quantifiers. This approach offers a new regard to what we call flexible reasoning. A uniform treatment of modulated logics is given here, obtaining some general results in model theory. Besides reviewing the “Logic of Ultrafilters”, which formalizes inductive assertions of the kind “almost all”, two new monotonic logical systems are proposed here, the “Logic of (...) Many” and the “Logic of Plausibility”, that characterize assertions of the kind “many”, and “for a good number of”. Although the notion of simple majority (“more than half”) can be captured by means of a modulated quantifier semantically interpreted by cardinal measure on evidence sets, it is proven that this system, although sound, cannot be complete if checked against the intended model. This justifies the interest on a purely qualitative approach to this kind of quantification, what is guaranteed by interpreting the modulated quantifiers as notions of families of principal filters and reduced topologies, respectively. We prove that both systems are conservative extensions of classical logic that preserve important properties, such as soundness and completeness. Some additional perspectives connecting our approach to flexible reasoning through modulated logics to epistemology and social choice theory are also discussed. (shrink)

When describing motion along both the horizontal and vertical axes, languages from different families express the elements encoding verticality before those coding for horizontality (e.g., going up right instead of right up). In light of the motor grounding of language, the present study investigated whether the prevalence of verticality in Path expression also governs the trajectory of arm biological movements. Using a 3D virtual-reality setting, we tracked the kinematics of hand pointing movements in five spatial directions, two of which implied (...) the vertical and horizontal vectors equally (i.e., up right +45° and bottom right −45°). Movement onset could be prompted by visual or auditory verbal cues, the latter being canonical in French (“en haut à droite”/up right) or not (“à droite en haut”/right up). In two experiments, analyses of the index finger kinematics revealed a significant effect of gravity, with earlier acceleration, velocity, and deceleration peaks for upward (+45°) than downward (−45°) movements, irrespective of the instructions. Remarkably, confirming the linguistic observations, we found that vertical kinematic parameters occurred earlier than horizontal ones for upward movements, both for visual and congruent verbal cues. Non-canonical verbal instructions significantly affected this temporal dynamic: for upward movements, the horizontal and vertical components temporally aligned, while they reversed for downward movements where the kinematics of the vertical axis was delayed with respect to that of the horizontal one. This temporal dynamic is so deeply anchored that non-canonical verbal instructions allowed for horizontality to precede verticality only for movements that do not fight against gravity. Altogether, our findings provide new insights into the embodiment of language by revealing that linguistic path may reflect the organization of biological movements, giving priority to the vertical axis. (shrink)

Ontologies aim to represent what is general, by means of universal statements. In contrast, dispositional predications capture knowledge about what is likely to happen if a certain set of circumstances obtain, which is crucial in investigative research such as in drug discovery and systems biology, where entities which are constitutionally dissimilar can nevertheless have similar behavior in a biological context. While such dispositional properties are increasingly included in biomedical ontologies, the circumstances under which the dispositions are realized are seldom explicitly (...) modeled, and doing so is problematic due to the necessary restriction to binary relations in OWL ontologies. In this paper we address this shortcoming, focusing on the bioactivity of small molecules at varying levels of concentration within a living organism as our problem domain, although our approach is generalizable to other problems. We discuss the ontological nature and representation of dispositions and their realization; consider the nature of concentrations and their representation; and finally we detail an approach to linking dispositions to the conditions for their realization which regards conditions as triggers for the process in which the disposition is realized. (shrink)

Despite being fairly powerful, finite non-deterministic matrices are unable to characterize some logics of formal inconsistency, such as those found between mbCcl and Cila. In order to overcome this limitation, we propose here restricted non-deterministic matrices (in short, RNmatrices), which are non-deterministic algebras together with a subset of the set of valuations. This allows us to characterize not only mbCcl and Cila (which is equivalent, up to language, to da Costa's logic C_1) but the whole hierarchy of da Costa's calculi (...) C_n. This produces a novel decision procedure for these logics. Moreover, we show that the RNmatrix semantics proposed here induces naturally a labelled tableau system for each C_n, which constitutes another decision procedure for these logics. This new semantics allows us to conceive da Costa's hierarchy of C-systems as a family of (non deterministically) (n+2)-valued logics, where n is the number of "inconsistently true" truth-values and 2 is the number of "classical" or "consistent" truth-values, for every C_n. (shrink)

This study has two goals. First, we present much‐needed empirical linguistic data and systematic analyses on the spatial semantic systems in English and Korean, two languages that have been extensively compared to date in the debate on spatial language and spatial cognition. We conduct our linguistic investigation comprehensively, encompassing the domains of tight‐ and loose‐fit as well as containment and support relations. The current analysis reveals both cross‐linguistic commonalities and differences: From a common set of spatial features, each language highlights (...) a subset of those features for its principal categorization, and those primary features are importantly different between English and Korean: English speakers categorize events predominantly by containment and support relations (and do so with prepositions), whereas Korean speakers categorize them by tight‐fit and loose‐fit relations (and do so with verbs), with a further distinction of containment and support within the loose‐fit relation. The analysis also shows that the tight‐fit domain is more cross‐linguistically diverse in categorization than is the loose‐fit domain. Second, we test the language data against the nonlinguistic categorization results reported in Choi and Hattrup (2012). The results show a remarkable degree of convergence between the patterns predicted from the current linguistic analysis and those found in C&H's nonlinguistic study and thus provide empirical and strong evidence for an influence of language on nonlinguistic spatial cognition. At the same time, the study reveals areas where the two systems closely interact with each other as well as those where one is independent from the other. Taking both parts of the study together, we identify the specific roles that language and spatial perception/cognition play in spatial categorization. (shrink)

In the tradition of Denotational Semantics one usually lets program constructs take their denotations in reflexive domains, i.e. in domains where self-application is possible. For the bulk of programming constructs, however, working with reflexive domains is an unnecessary complication. In this paper we shall use the domains of ordinary classical type logic to provide the semantics of a simple programming language containing choice and recursion. We prove that the rule of {\em Scott Induction\/} holds in this new setting, (...) prove soundness of a Hoare calculus relative to our semantics, give a direct calculus ${\cal C}$ on programs, and prove that the denotation of any program $P$ in our semantics is equal to the union of the denotations of all those programs $L$ such that $P$ follows from $L$ in our calculus and $L$ does not contain recursion or choice. (shrink)

By means of models in toposes of C-sets (where C is a small category), necessary conditions are found for the minimum quantified extension of a propositional (intermediate, modal) logic to be complete with respect to Kripke semantics; in particular, many well-known systems turn out to be incomplete.

Lewis, D. Semantic analyses for dyadic deontic logic.--Salomaa, A. Some remarks concerning many-valued propositional logics.--Chellas, B. F. Conditional obligation.--Jeffrey, R.C. Remarks on interpersonal utility theory.--Hintikka, J. On the proper treatment of quantifiers in Montague semantics.--Mayoh, B.H. Extracting information from logical proofs.--Åqvist, L. A new approach to the logical theory of actions and causality.--Pörn, I. Some basic concepts of action.--Bouvère, K. de. Some remarks concerning logical and ontological theories.--Hacking, I. Combined evidence.--Äberg, C. Solution to a problem raised by Stig Kanger (...) and a set theoretical statement equivalent to the axiom of choice.--Lindström, P. On characterizing elementary logic.-- Scott, D. Rules and derived rules.--Hansson, B. A program for pragmatics.--Hermerén, G. Models.--Fenstad, J.E. Remarks on logic and probability.--Stenlund, S. Analytic and synthetic arithmetical statements. (shrink)

Recent semantic approaches to scientific structuralism, aiming to make precise the concept of shared structure between models, formally frame a model as a type of set-structure. This framework is then used to provide a semantic account of (a) the structure of a scientific theory, (b) the applicability of a mathematical theory to a physical theory, and (c) the structural realist’s appeal to the structural continuity between successive physical theories. In this paper, I challenge the idea that, to be so used, (...) the concept of a model and so the concept of shared structure between models must be formally framed within a single unified framework, set-theoretic or other. I first investigate the Bourbaki-inspired assumption that structures are types of set-structured systems and next consider the extent to which this problematic assumption underpins both Suppes’ and recent semantic views of the structure of a scientific theory. I then use this investigation to show that, when it comes to using the concept of shared structure, there is no need to agree with French that “without a formal framework for explicating this concept of ‘structure-similarity’ it remains vague, just as Giere’s concept of similarity between models does ...” (French, 2000, Synthese, 125, pp. 103–120, p. 114). Neither concept is vague; either can be made precise by appealing to the concept of a morphism, but it is the context (and not any set-theoretic type) that determines the appropriate kind of morphism. I make use of French’s (1999, From physics to philosophy (pp. 187–207). Cambridge: Cambridge University Press) own example from the development of quantum theory to show that, for both Weyl and Wigner’s programmes, it was the context of considering the ‘relevant symmetries’ that determined that the appropriate kind of morphism was the one that preserved the shared Lie-group structure of both the theoretical and phenomenological models. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:russell: the Journal of Bertrand Russell Studies n.s. 34 (summer 2014): 67–78 The Bertrand Russell Research Centre, McMaster U. issn 0036–01631; online 1913–8032 c:\users\kenneth\documents\type3401\rj 3401 193 red.docx 2014-05-14 8:54 PM aiscussion THE STRUCTURE, SEMANTICS, AND USE OF DESCRIPTIONS Jolen Galaugher Philosophy / McMaster U. Hamilton, on, Canada l8s 4l6 [email protected] / [email protected] he division of designators into denoting expressions and referring expressions has become a familiar feature of (...) the Russellian orthodoxy in the philosophy of language. At a glance, expressions of the referring kind seem to be unstructured, lacking independently meaningful proper parts, while those of the denoting kind seem to be structured quantifiers, having molecular complexity. Most examples fit this pattern: proper names, indexicals, and demonstratives are unstructured, while definite descriptions and other quanti fier phrases are typically structured. On Russell’s 1903 theory of denoting, the semantic structure (independently meaningful proper parts) of denoting complexes had proved a source of difficulty for his logic of propositions. The early theory was not only incapable of explaining both how we are supposed to designate complex meanings and how complex meanings are supposed to denote, but was also at odds with the view that proposition and constituent are logically basic, introducing further functional complexes into the propositional complex. Russell’s 1905 theory of descriptions reconstrued these apparently structured referring expressions as quantified noun phrases. On the new theory, knowing the meaning of such expressions does not require acquaintance with a specific object, but rather a grasp of the truth-conditions of the sentences in which they occur.1 One might say that on the new theory, denoting is linked to object-independent truth-conditions, while referring is linked to object-dependent truth-conditions—a connection elaborated and extended by Kripke and Kaplan. This is the situation as Arthur Sullivan paints it in his new book, Reference and Structure in the Philosophy of Language: a Defense of the 1 Russell articulated the dichotomy in “Knowledge by Acquaintance and Knowledge by Description” (1911), ML, p. 226; Papers 6: 158. For Sullivan’s use of this passage, see his anthology, Logicism and the Philosophy of Language, pp. 79–80, and Reference and Structure in the Philosophy of Language, pp. 13–14, 137, 140 n.15. q= 68 Discussion c:\users\kenneth\documents\type3401\rj 3401 193 red.docx 2014-05-14 8:54 PM Russellian Orthodoxy (2013). In this work, Arthur Sullivan defends a stronger set of claims than the denoting /referring distinction might historically have entailed. Building on Neale’s sharp distinction between semantically unstructured rigid referring expressions and semantically structured restricted quantifiers,2 Sullivan takes it to be crucial that these categories are exhaustive and exclusive, so that all and only referring expressions are unstructured designators, and all and only denoting expressions are structured designators (p. 13). Adopting a distinction from Bach,3 Sullivan maintains that the semantic mechanism of referring designators is simply to conventionally relate the utterance of the designator to the designatum, and hence to express object-dependent propositions, while the semantic mechanism of denoting designators is satisfactional, expressing a compositional condition which may or may not be satisfied by any object and which thus expresses object-independent propositions (p. 11). In Part 1, Sullivan articulates the orthodox theory of reference in terms of these two exhaustive and exclusive categories of designator and the distinct, corresponding semantic mechanisms by which they designate. In Part 2, he provides arguments in favour of the orthodoxy. In Part 3, he deals with apparent counter -examples, reinterpreting complex demonstratives and referential uses of definite descriptions to bring them into conformity with the strict referringversus -denoting dichotomy. In Part 4, he offers a synopsis and some general conclusions. Importantly, in Part 2, Sullivan argues that semantic structure is a necessary but not sufficient condition of non-rigidity, that only denoting designnators are non-rigid, that all unstructured designators are rigid designators, and that the lack of semantic structure is necessary and sufficient for status as a referring expression. Contrary to the view which is now popular, Russell regarded ordinary proper names as... (shrink)

The authors of Austere Realism describe and defend a provocative ontological-cum-semantic position, asserting that the right ontology is minimal or austere, in that it excludes numerous common-sense posits, and that statements employing such posits are nonetheless true, when truth is understood to be semantic correctness under contextually operative semantic standards. Terence Horgan and Matjaz [hacek over z] Potrc [hacek over c] argue that austere realism emerges naturally from consideration of the deep problems within the naive common-sense approach to truth and (...) ontology. They offer an account of truth that confronts these deep internal problems and is independently plausible: contextual semantics, which asserts that truth is semantically correct affirmability. Under contextual semantics, much ordinary and scientific thought and discourse is true because its truth is indirect correspondence to the world. After offering further arguments for austere realism and addressing objections to it, Horgan and Potrc [hacek over c] consider various alternative austere ontologies. They advance a specific version they call "blobjectivism"--the view that the right ontology includes only one concrete particular, the entire cosmos, which, although it has enormous local spatiotemporal variability, does not have any proper parts. The arguments in Austere Realism are powerfully made and concisely and lucidly set out. The authors' contentions and their methodological approach--products of a decade-long collaboration--will generate lively debate among scholars in metaphysics, ontology, and philosophy. Terence E. Horgan is Professor of Philosophy at the University of Arizona. Matjaz [hacek over z] Potrc [hacek over c] is Professor of Philosophy at the University of Ljubljana. (shrink)

This paper describes a novel pedagogical software program that can be seen as an online companion to one of the standard textbooks of formal natural language semantics, Heim and Kratzer (1998). The Penn Lambda Calculator is a multifunctional application designed for use in standard graduate and undergraduate introductions to formal semantics: Teachers can use the application to demonstrate complex semantic derivations in the classroom and modify them interactively, and students can use it to work on problem sets provided (...) by the teacher. The program supports demonstrations and exercises in two main areas: (1) performing beta reduction in the simply typed lambda calculus; (2) application of the bottom-up algorithm for computing the compositional semantics of natural language syntax trees. The program is able to represent the full range of phenomena covered in the Heim and Kratzer textbook by function application, predicate modification, and lambda abstraction. This includes phenomena such as intersective adjectives, relative clauses and quantifier raising. In the student use case, emphasis has been placed on providing “live” feedback for incorrect answers. Heuristics are used to detect the most frequent student errors and to return specific, interactive suggestions. (shrink)

A structure A for the language L, which is the first-order language (without equality) whose only nonlogical symbol is the binary predicate symbol , is called a quasi -struoture iff (a) the universe A of A consists of sets and (b) a b is true in A ([p) a = {p } & p b] for every a and b in A, where a(b) is the name of a (b). A quasi -structure A is called an -structure iff (c) {p (...) } A whenever p a A. Then a closed formula in L is derivable from Leniewski's axiom x, y[x y u (u x) u; v(u, v x u v) u(u x u y)] (from the axiom x, y(x y x x) x, y, z(x y z y x z)) iff is true in every -structure (in every quasi -structure). (shrink)

This paper sets out a semantics for C.I. Lewis's logic S2 based on the ontology of his 1923 paper ‘Facts, Systems, and the Unity of the World’. In that article, worlds are taken to be maximal consistent systems. A system, moreover, is a collection of facts that is closed under logical entailment and conjunction. In this paper, instead of defining systems in terms of logical entailment, I use certain ideas in Lewis's epistemology and philosophy of logic to define a (...) class of models in which systems are taken to be primitive elements but bear certain relations to one another. I prove soundness and completeness for S2 over this class of models and argue that this semantics makes sense of at least a substantial fragment of Lewis's logical theory. (shrink)

Canonical extension has proven to be a powerful tool in algebraic study of propositional logics. In this paper we describe a generalisation of the theory of canonical extension to the setting of first order logic. We define a notion of canonical extension for coherent categories. These are the categorical analogues of distributive lattices and they provide categorical semantics for coherent logic, the fragment of first order logic in the connectives ∧, ∨, 0, 1 and ∃. We describe a universal (...) property of our construction and show that it generalises the existing notion of canonical extension for distributive lattices. Our new construction for coherent categories has led us to an alternative description of the topos of types, introduced by Makkai in [22]. This allows us to give new and transparent proofs of some properties of the action of the topos of types construction on morphisms. Furthermore, we prove a new result relating, for a coherent category C, its topos of types to its category of models. (shrink)

Semantics plays a role in grammar in at least three guises. (A) Linguists seek to account for speakers‘ knowledge of what linguistic expressions mean. This goal is typically achieved by assigning a model theoretic interpretation in a compositional fashion. For example, *No whale flies* is true if and only if the intersection of the sets of whales and fliers is empty in the model. (B) Linguists seek to account for the ability of speakers to make various inferences based on (...) semantic knowledge. For example, *No whale flies* entails *No blue whale flies* and *No whale flies high*. (C) The wellformedness of a variety of syntactic constructions depends on morpho-syntactic features with a semantic flavor. For example, *Under no circumstances would a whale fly* is grammatical, whereas *Under some circumstances would a whale fly* is not, corresponding to the downward vs. upward monotonic features of the preposed phrases. It is usually assumed that once a compositional model theoretic interpretation is assigned to all expressions, its fruits can be freely enjoyed by inferencing and syntax. What place might proof theory have in this picture? (shrink)

Bypassing Lewis’ Triviality Results. A Kripke-Style Partial Semantics for Compounds of Adams’ Conditionals Alberto Mura University of Sassari Abstract According to Lewis’ Triviality Results (LTR), conditionals cannot satisfy the equa­tion (E) P(C if A) = P(C | A), except in trivial cases. Ernst Adams (1975), however, provided a probabilistic semantics for the so-called simple conditionals that also sat­isfies equation (E) and provides a probabilistic counterpart of logical consequence (called p-entailment). Adams’ probabilistic semantics is coextensive to Stalnaker­Thomason’s (1970) (...) and Lewis’ (1973) semantics as far as simple conditionals are concerned. A theorem, proved in McGee 1981, shows that no truth-functional many-valued logic allows a relation of logical consequence coextensive with Adams’ p-entailment. This paper presents a modified modal (Kripke-style) version of de Finetti’s se­mantics that escapes McGee’s result and provides a general truth-conditional se­mantics for indicative conditionals. It agrees with Adams’ logic and is not affected by LTR. The new framework encompasses and extends Adams’ probabilistic se­mantics (APS) to compounds of conditionals. A generalised set of axioms for prob­ability over the set of tri-events is provided, which coincide with the standard axioms over the set of the two-valued ordinary sentences. -/- Keywords: Conditionals, Probability logic, de Finetti, Tri-events, Adams’ logic, Stal­naker’s thesis, Partial logic, Lewis’ triviality results, Ramsey test. (shrink)

Heim 1983 suggested that the analysis of presupposition projection requires that the classical notion of meanings as truth conditions be replaced with a dynamic notion of meanings as Context Change Potentials. But as several researchers (including Heim herself) later noted, the dynamic framework is insufficiently predictive: although it allows one to state that, say, the dynamic effect of F and G is to first update a Context Set C with F and then with G (i.e., C[F and G] = C[F][G]), (...) it fails to explain why there couldn’t be a ‘deviant’ conjunction and* which performed these operations in the opposite order (i.e., C[F and* G] = C[G][F]). We provide a formal introduction to a competing framework, the Transparency theory, which addresses this problem. Unlike dynamic semantics, our analysis is fully classical, i.e., bivalent and static. And it derives the projective behavior of connectives from their bivalent meaning and their syntax. We concentrate on the formal properties of a simple version of the theory, and we prove that (i) full equivalence with Heim’s results is guaranteed in the propositional case (Theorem 1), and that (ii) the equivalence can be extended to the quantificational case (for any generalized quantifiers), but only when certain conditions are met (Theorem 2). (shrink)