This paper embeds the core part of Discourse Representation Theory in the classical theory of types plus a few simple axioms that allow the theory to express key facts about variables and assignments on the object level of the logic. It is shown how the embedding can be used to combine core analyses of natural language phenomena in Discourse Representation Theory with analyses that can be obtained in Montague Semantics.

The paper shows how ideas that explain the sense of an expression as a method or algorithm for finding its reference, preshadowed in Frege’s dictum that sense is the way in which a referent is given, can be formalized on the basis of the ideas in Thomason (1980). To this end, the function that sends propositions to truth values or sets of possible worlds in Thomason (1980) must be replaced by a relation and the meaning postulates governing the behaviour of (...) this relation must be given in the form of a logic program. The resulting system does not only throw light on the properties of sense and their relation to computation, but also shows circular behaviour if some ingredients of the Liar Paradox are added. The connection is natural, as algorithms can be inherently circular and the Liar is explained as expressing one of those. Many ideas in the present paper are closely related to those in Moschovakis (1994), but receive a considerably lighter formalization. (shrink)

In this paper we consider the theory of predicate logics in which the principle of Bivalence or the principle of Non-Contradiction or both fail. Such logics are partial or paraconsistent or both. We consider sequent calculi for these logics and prove Model Existence. For L4, the most general logic under consideration, we also prove a version of the Craig-Lyndon Interpolation Theorem. The paper shows that many techniques used for classical predicate logic generalise to partial and paraconsistent logics once the right (...) set-up is chosen. Our logic L4 has a semantics that also underlies Belnap’s [4] and is related to the logic of bilattices. L4 is in focus most of the time, but it is also shown how results obtained for L4 can be transferred to several variants. (shrink)

The paper develops Lambda Grammars, a form of categorial grammar that, unlike other categorial formalisms, is non-directional. Linguistic signs are represented as sequences of lambda terms and are combined with the help of linear combinators.

In this paper we discuss a new perspective on the syntax-semantics interface. Semantics, in this new set-up, is not ‘read off’ from Logical Forms as in mainstream approaches to generative grammar. Nor is it assigned to syntactic proofs using a Curry-Howard correspondence as in versions of the Lambek Calculus, or read off from f-structures using Linear Logic as in Lexical-Functional Grammar (LFG, Kaplan & Bresnan [9]). All such approaches are based on the idea that syntactic objects (trees, proofs, fstructures) are (...) somehow prior and that semantics must be parasitic on those syntactic objects. We challenge this idea and develop a grammar in which syntax and semantics are treated in a strictly parallel fashion. The grammar will have many ideas in common with the (converging) frameworks of categorial grammar and LFG, but its treatment of the syntax-semantics interface is radically different. Also, although the meaning component of the grammar is a version of Montague semantics and although there are obvious affinities between Montague’s conception of grammar and the work presented here, the grammar is not compositional, in the sense that composition of meaning need not follow surface structure. (shrink)

Bd. 1. 1791-1794.--Bd. 2. 1793-1795.--Bd. 3.--1794-1796.--Bd. 4. 1797-1798.--Bd. 5. 1798-1799.--Bd. 6. 1799-1800.--Bd. 7. 1800-1801.--Bd. 8. 1801-1806.--Bd. 9. 1806-1807.--Bd. 10. 1808-1812.

This paper developes a relational---as opposed to a functional---theory of types. The theory is based on Hilbert and Bernays' eta operator plus the identity symbol, from which Church's lambda and the other usual operators are then defined. The logic is intended for use in the semantics of natural language.

Taking the lead from orthodox quantum theory, I will introduce a handy generalization of the Boolean approach to propositions and questions: the orthoalgebraic framework. I will demonstrate that this formalism relates to a formal theory of questions (or ‘observables’ in the physicist’s jargon). This theory allows formulating attitude questions, which normally are non-commuting, i.e., the ordering of the questions affects the answer behavior of attitude questions. Further, it allows the expression of conditional questions such as “If Mary reads the book, (...) will she recommend it to Peter?”, and thus gives the framework the semantic power of raising issues and being informative at the same time. In the case of commuting observables, there are close similarities between the orthoalgebraic approach to questions and the Jäger/Hulstijn approach to question semantics. However, there are also differences between the two approaches even in case of commuting observables. The main difference is that the Jäger/Hulstijn approach relates to a partition theory of questions whereas the orthoalgebraic approach relates to a ‘decorated’ partition theory (i.e. the elements of the partition are decorated by certain semantic values). Surprisingly, the orthoalgebraic approach is able to overcome most of the difficulties of the Jäger/Hulstijn approach. Furthermore, the general approach is suitable to describe the different types of (non-commutative) attitude questions as investigated in modern survey research. Concluding, I will suggest that an active dialogue between the traditional model-theoretic approaches to semantics and the orthoalgebraic paradigm is mandatory. (shrink)

Small wonder: finitude and its horizons -- The underside of modernity: Adorno, Heidegger, and Dussel -- Empire or cosmopolis: civilization at the crossroads -- Confronting empire: a tribute to Arundhati Roy -- Speaking truth to power: in memory of Edward Said -- Critical intellectuals in a global age: toward a global public sphere -- Social identity and creative praxis: hommage á Merleau-Ponty -- Nature and artifact: Gadamer on human health -- Borders or horizons?: an older debate revisited -- Empire and (...) faith: sacred non-sovereignty -- Appendix: A. The dignity of difference: a salute to Jonathan Sacks -- B. Religion and rationality: Habermas and the early Frankfurt school -- Nomolatry and fidelity: a response to Charles Taylor. (shrink)

Ambiguities in natural language can multiply so fast that no person or machine can be expected to process a text of even moderate length by enumerating all possible disambiguations. A sentence containing $n$ scope bearing elements which are freely permutable will have $n!$ readings, if there are no other, say lexical or syntactic, sources of ambiguity. A series of $m$ such sentences would lead to $(n!)^m$ possibilities. All in all the growth of possibilities will be so fast that generating readings (...) first and testing their acceptability afterwards will not be feasible. -/- This insight has led a series of researchers to adopt a level of representation at which ambiguities remain unresolved. The idea here is not to generate and test many possible interpretations but to first generate one `underspecified' representation which in a sense represents all its complete specifications and then use whatever information is available to further specify the result. -/- One central hypothesis in the paper will be that the relation between an underspecified representation and its full representations is not so much the relation between one structure and a set of other structures but is in fact the relation between a description (a set of logical sentences) and its models. (shrink)

There are two kinds of semantic theories of anaphora. Some, such as Heim’s File Change Semantics, Groenendijk and Stokhof’s Dynamic Predicate Logic, or Muskens’ Compositional DRT (CDRT), seem to require full coindexing of anaphora and their antecedents prior to interpretation. Others, such as Kamp’s Discourse Representation Theory (DRT), do not require this coindexing and seem to have an important advantage here. In this squib I will sketch a procedure that the first group of theories may help themselves to so that (...) they can interleave interpretation and coindexing in DRT’s way. (shrink)

Tiere haben erstaunliche kognitive Fähigkeiten, ein diesen Fähigkeiten entsprechendes Bewußtsein und Formen des Selbstbewußtseins. Das Denken in diskreten Einheiten von Urteilen scheint ihnen jedoch nicht zugänglich zu sein, damit auch nicht die Unterscheidung von Bejahung und Verneinung und von wahr und falsch. Wie ist das Denken und damit das objektive Erkennen beim Menschen entstanden? Welche Rolle spielt das Gehirn bei Mensch und Tier? Wir Menschen leben in zwei Welten, die paradoxerweise zugleich eine ist. Das Tageslicht, Gerüche, die Hauswand, an der (...) wir entlanggehen und die wir nicht durchschreiten können diese unsere Lebenswelt unterscheidet sich zunächst nicht von der des Hundes, der uns begleitet. Tiere nehmen sinnlich wahr wie wir, sie erschrecken wie wir bei einem lauten Geräusch, sie zeigen dieselbe freudige Erregung wie wir. Zugleich gibt es für uns eine andere, wiewohl identische Welt, von der die Tiere offenbar nichts wissen: Wir Menschen machen die Dinge zu Objekten der Erkenntnis; dieselbe Sonne, die uns blendet und die sich im Tageslauf langsam von Osten nach Westen bewegt, steht, so erkennen wir, fest im Zentrum des Planetensystems. Wir spüren die Kälte, aber wir erkennen in ihr zugleich die Ursache der Eisbildung; kein Tier weiß, was eine Ursache ist, kein Tier kann sich wundern, und auch denken kann es nicht. These: Natürlich können Tiere denken. "Ach, Sie werden es nicht glauben, aber unser Leo versteht jedes Wort." Gegenthese: Natürlich können Tiere nicht denken. Es fehlen ihnen vor allem zwei Voraussetzungen des Urteilens und Denkens: Sie verfügen über keine geeigneten Begriffe, und sie kennen keine gemeinsame Öffentlichkeit, die durch das Zeigen geschaffen und im Urteil vertieft wird. (shrink)

The revival of action based explanations as well as their formal structuring have been two of the most important topics within explanatory sociology since the 1980s. The two newly developed approaches, being structural individualism and analytical sociology based on mechanism models, will be outlined in this article. The article is dedicated to a comparison of the aims and the formal structure of both approaches. It is shown that explanations within analytical sociology tend to be more realistic but also more complex. (...) They do not differentiate between micro and macro levels in analytical terms and use micro mechanisms instead of an analytically strong action theory that makes it difficult to systemize mechanism models. On the other hand, structural individualistic explanations that use a general action law from which social interdependencies are to be interpreted as an opportunity structure can formulate a default-option from which models can be expanded and also worked out to mechanism types. (shrink)

In this paper we summarize some results about sets in Frege structures. The resulting set theory is discussed with respect to its historical and philosophical significance. This includes the treatment of diagonalization in the presence of a universal set.

We study the logical relationship of various forms of induction, as well as quantification operators in applicative theories. In both cases the introduced notion of $\hbox{\sf N}$ -strictness allows us to obtain the appropriate results.

An attractive way to model the relation between an underspecified syntactic representation and its completions is to let the underspecified representation correspond to a logical description and the completions to the models of that description. This approach, which underlies the Description Theory of Marcus et al. 1983 has been integrated in Vijay-Shanker 1992 with a pure unification approach to Lexicalized Tree-Adjoining Grammars (Joshi et al. 1975, Schabes 1990). We generalize Description Theory by integrating semantic information, that is, we propose to (...) tackle both syntactic and semantic underspecification using descriptions. (shrink)

Type-logical semantics studies linguistic meaning with the help of the theory of types. The latter originated with Russell as an answer to the paradoxes, but has the additional virtue that it is very close to ordinary language. In fact, type theory is so much more similar to language than predicate logic is, that adopting it as a vehicle of representation can overcome the mismatches between grammatical form and predicate logical form that were observed by Frege and Russell. The grammatical forms (...) of ordinary language sentences consequently may be taken to be much less misleading than logicians in the first half of the 20th century often thought them to be. This was realized by Richard Montague, who used the theory of types to translate fragments of ordinary language into a logical language. Semantics is commonly divided into lexical semantics, which studies the meaning of words, and compositional semantics, which studies the way in which complex phrases obtain a meaning from their constituents. The strength of type-logical semantics lies with the latter, but type-logical theories can be combined with many competing hypotheses about lexical meaning, provided these hypotheses are expressed using the language of type theory. (shrink)

In mathematical languages and in predicate logic coreferential terms can be interchanged in any sentence without altering the truth value of that sentence. Replacing 3 + 5 by 12 − 4 in any formula of arithmetic will never lead from truth to falsity or from falsity to truth. But natural languages are different in this respect. While in some contexts it is always allowed to interchange coreferential terms, other contexts do not admit this. An example of the first sort of (...) context is likes bananas: for any two coreferential noun phrases A and B the sentence A likes bananas is true if and only if B likes bananas is. A context that does not allow intersubstitution of coreferents is The Ancients knew that appears at dawn. If we fill the hole with the noun phrase the Morning Star we get the true (1a), while if we plug in the Evening Star we get the false (1b). Yet the Morning Star and the Evening Star both refer to the planet Venus and are thus coreferential. (shrink)

Logic has its roots in the study of valid argument, but while traditional logicians worked with natural language directly, modern approaches first translate natural arguments into an artificial language. The reason for this step is that some artificial languages now have very well developed inferential systems. There is no doubt that this is a great advantage in general, but for the study of natural reasoning it is a drawback that the original linguistic forms get lost in translation. An alternative approach (...) would be to develop a general theory of the natural logic behind human reasoning and human information processing by studying formal logics that operate directly on linguistic representations. That this is possible we will try to make plausible in this paper. It will turn out that one level of representation, that of Logical Form, can meaningfully be identified with the language of an existing and well-understood logic, a restricted form of the theory of types. It is not difficult to devise inference systems for this language, and it is thus possible to study reasoning systems that are based directly on language. (shrink)

This paper argues for the idea that in describing language we should follow Haskell Curry in distinguishing between the structure of an expression and its appearance or manifestation . It is explained how making this distinction obviates the need for directed types in type-theoretic grammars and a simple grammatical formalism is sketched in which representations at all levels are lambda terms. The lambda term representing the abstract structure of an expression is homomorphically translated to a lambda term representing its manifestation, (...) but also to a lambda term representing its semantics. (shrink)

Democracy purged of all its Disadvantages. « Encoded at the level of its lexicology and logical constructedness, the republican discourse of the enlightenment and revolution is marked by two conceptualizations which contradict and mutually exclude each other. Contemporary observers of the revolution or those close to its events speak about an opposition between an order of egotism and an order of equality, between a principle of utility and a principle of ascetism, between an ethics based on personal interest and an (...) ethics based on the national interest, between a kind of individualism and a kind of socialism, etc. Because it has excluded physiocratic thinking from its domain, the traditional historio-graphy of political ideas has obstructed an unbiased view to the context which engenders conceptualizations of an alternative Republicanism vis-a-vis that of Rousseau, while at the same time utilizing Rousseaus formulas ». (shrink)

'Nun aber kam die Kritik der Urteilskraft mir zuhanden, und dieser bin ich eine höchst frohe Lebensepoche schuldig.' (Goethe, 1817) In der Epoche der klassischen deutschen Philosophie galt Kants 'Kritik der Urteilskraft' beim gelehrten Publikum als 'beliebteste' Kantschrift. Heute wird sie weitestgehend fragmentarisch und mit einem deutlichen Schwerpunkt auf der Kritik der ästhetischen Urteilskraft gelesen. Obwohl sich der vorliegende Sammelband der gesamten dritten Kritik widmet, versuchen die Autoren insbesondere einen verstärkten Diskurs über Kants Kritik der teleologisch reflektierenden Urteilskraft in Gang (...) zu setzen. Denn für Kant vermag nur eine wohlverstandene kritisch reflektierte Teleologie die Einheit der endlichen Vernunft denkbar zu machen und damit die Transzendentalphilosophie zu vollenden. (shrink)