An algebraic type of structure is shown forth which is such that if it is a characteristic matrix for a logic, then that logic satisfies Meyer's weak variable sharing property. As a corollary, it is shown that RM and all its odd-valued extensions $\mathbf{RM}_{2n\mathord{-}1}$ satisfy the weak variable sharing property. It is also shown that a proof to the effect that the "fuzzy" version of the relevant logic R satisfies the property is incorrect.

As is well known, the variable-sharing property (vsp) is, according to Anderson and Belnap, a necessary property of any relevant logic. In this paper, we shall consider two versions of the vsp, what we label the "weak vsp" (wvsp) and the "strong vsp" (svsp). In addition, the "no loose pieces property," a property related to the wvsp and the svsp, will be defined. Each one of these properties shall generally be characterized by means of (...) a class of logical matrices. In this way, any logic verified by an actual matrix in one of these classes has the property the class generally represents. Particular matrices (and so, logics) in each class are provided. (shrink)

As it is well known, Relevance Logic R plus the axiom mingle (R-Mingle) does not have the variable-sharing property (vsp). The aim of this paper is to improve this result by defining a weak logic with the axiom mingle and not included in minimal logic BM lacking the vsp.

The logic TM is the result of adding the mingle axiom, M to Ticket Entailment logic, T. In the present study, it is proved that TM has the variable-sharing property . Ternary relational semantics for TM is provided. Finally, an interesting extension of TM with the vsp is briefly discussed.

In our paper “A general characterization of the variable-sharing property by means of logical matrices”, a general class of so-called “Relevant logical matrices”, RMLs, is defined. The aim of this paper is to define a class of simpler Relevant logical matrices RMLs′serving the same purpose that RMLs, to wit: any logic verified by an RML′has the variable-sharing property and related properties predicable of the logic of entailment E and of the logic of relevance R.

Many relevant logics are conservatively extended by Boolean negation. Not all, however. This paper shows an acute form of non-conservativeness, namely that the Boolean-free fragment of the Boolean extension of a relevant logic need not always satisfy the variable-sharing property. In fact, it is shown that such an extension can in fact yield classical logic. For a vast range of relevant logic, however, it is shown that the variable-sharing property, restricted to the Boolean-free fragment, (...) still holds for the Boolean extended logic. (shrink)

A restriction of R-Mingle with the variable-sharing property and the Ackermann properties is defined. From an intuitive semantical point of view, this restriction is an alternative to Anderson and Belnap’s logic of entailment E.

We characterize the non-trivial substructural logics having the variable sharing property as well as its strong version. To this end, we find the algebraic counterparts over varieties of these logical properties. -/- .

In this paper, we examine a number of relevant logics’ variable sharing properties from the perspective of theories of topic or subject-matter. We take cues from Franz Berto’s recent work on topic to show an alignment between families of variable sharing properties and responses to the topic transparency of relevant implication and negation. We then introduce and defend novel variable sharing properties stronger than strong depth relevance—which we call cn-relevance and lossless cn-relevance—showing that the (...) properties are satisfied by the weak relevant logics and , respectively. We argue that such properties address a sort of semantic lossiness of strong depth relevance. (shrink)

However broad or vague the notion of connexivity may be, it seems to be similar to the notion of relevance even when relevance and connexive logics have been shown to be incompatible to one another. Relevance logics can be examined by suggesting syntactic relevance principles and inspecting if the theorems of a logic abide to them. In this paper we want to suggest that a similar strategy can be employed with connexive logics. To do so, we will suggest some properties (...) that seem to be hinted at in Nelson’s work. Following this strategy will ideally shed some light over the notion of content and will also help make a clear comparison between relevance and connexive logics. (shrink)

A propositional logic has the variable sharing property if φ → ψ is a theorem only if φ and ψ share some propositional variable. In this note, I prove that positive semilattice relevance logic and its extension with an involution negation have the variable sharing property. Typical proofs of the variable sharing property rely on ad hoc, if clever, matrices. However, in this note, I exploit the properties of rather more (...) intuitive arithmetical structures to establish the variable sharing property for the systems discussed. (shrink)

Relevant logics infamously have the property that they only validate a conditional when some propositional variable is shared between its antecedent and consequent. This property has been strengthened in a variety of ways over the last half-century. Two of the more famous of these strengthenings are the strong variable sharing property and the depth relevance property. In this paper I demonstrate that an appropriate class of relevant logics has a property that might (...) naturally be characterized as the supremum of these two properties. I also show how to use this fact to demonstrate that these logics seem to be constructive in previously unknown ways. (shrink)

The concept of shared mental models refers to the shared understanding among team members about how they should behave in different situations. This article aimed to develop a new shared mental model measure, specifically designed for the refereeing context. A cross-sectional study was conducted with three samples: national and regional football referees (n = 133), national football referees and assistant referees and national futsal referees (n = 277), and national futsal referees (n = 60). The proposed version of the Referee (...) Shared Mental Models Measure (RSMMM) has 13 items that are reflected on a single factor structure. The RSMMM presented good validity evidence both based on the internal structure and based on relations to other variables (presenting positive associations with team work engagement, team adaptive performance, and team effectiveness). Such promising psychometric properties point to an optimistic outlook regarding its use to measure shared mental models in futsal and football referee teams. -/- . (shrink)

Let R+ be the positive fragment of Anderson and Belnap’s Logic of Relevance, R. And let RMO+ be the result of adding the Mingle principle ) to R+. We have shown in [2] that either a minimal negation or else a semiclassical one can be added to RMO+ preserving the variable-sharing property. Moreover, each of there systems is given a semantics in the Routley-Meyer style. In describing in [2] the models for RMO+ plus minimal negation, we noted (...) that a similar strategy would give us a semantics for R+ with minimal negation; that is, constructive R. The aim of this paper is to prove this claim. (shrink)

The aim of this paper is technically to study Belnap's four-valued sentential logic . First, we obtain a Gentzen-style axiomatization of this logic that contains no structural rules while all they are still admissible in the Gentzen system what is proved with using some algebraic tools. Further, the mentioned logic is proved to be the least closure operator on the set of {Λ, V, ⌝}-formulas satisfying Tarski's conditions for classical conjunction and disjunction together with De Morgan's laws for negation. It (...) is also proved that Belnap's logic is the only sentential logic satisfying the above-mentioned conditions together with Anderson-Belnap's Variable-Sharing Property. Finally, we obtain a finite Hilbert-style axiomatization of this logic. As a consequence, we obtain a finite Hilbert-style axiomatization of Priest's logic of paradox. (shrink)

A situation, in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A (point-valued) solution for TU-games assigns a payoff distribution to every TU-game. In this article we discuss a class of equal surplus sharing solutions consisting of all convex combinations of the CIS-value, the ENSC-value and the equal division solution. We provide several characterizations of this class of solutions on variable (...) and fixed player set. Specifications of several properties characterize specific solutions in this class. (shrink)

In this article, I provide Urquhart-style semilattice semantics for three connexive logics in an implication-negation language (I call these “pure theories of connexive implication”). The systems semantically characterized include the implication-negation fragment of a connexive logic of Wansing, a relevant connexive logic recently developed proof-theoretically by Francez, and an intermediate system that is novel to this article. Simple proofs of soundness and completeness are given and the semantics is used to establish various facts about the systems (e.g., that two of (...) the systems have the variable sharing property). I emphasize the intuitive content of the semantics and discuss how natural informational considerations underly each of the examined systems. (shrink)

Relevant logics have traditionally been viewed as paraconsistent. This paper shows that this view of relevant logics is wrong. It does so by showing forth a logic which extends classical logic, yet satisfies the Entailment Theorem as well as the variable sharing property. In addition it has the same S4-type modal feature as the original relevant logic E as well as the same enthymematical deduction theorem. The variable sharing property was only ever regarded as (...) a necessary property for a logic to have in order for it to not validate the so-called paradoxes of implication. The Entailment Theorem on the other hand was regarded as both necessary and sufficient. This paper shows that the latter theorem also holds for classical logic, and so cannot be regarded as a sufficient property for blocking the paradoxes. The concept of suppression is taken up, but shown to be properly weaker than that of variable sharing. (shrink)

Different directed acyclic graphs may be Markov equivalent in the sense that they entail the same conditional independence relations among the observed variables. Chickering provided a transformational characterization of Markov equivalence for DAGs, which is useful in deriving properties shared by Markov equivalent DAGs, and, with certain generalization, is needed to prove the asymptotic correctness of a search procedure over Markov equivalence classes, known as the GES algorithm. For DAG models with latent variables, maximal ancestral graphs provide a neat representation (...) that facilitates model search. However, no transformational characterization -- analogous to Chickering's -- of Markov equivalent MAGs is yet available. This paper establishes such a characterization for directed MAGs, which we expect will have similar uses as it does for DAGs. (shrink)

Relevant propositional dynamic logics have been sporadically discussed in the broader context of modal relevant logics, but have not come up for sustained investigation until recently. In this paper, we develop a philosophical motivation for these systems, and present some new results suggested by the proposed motivation. Among these, we’ll show how to adapt some recent work to show that the extensions of relevant logics by the extensional truth constants \ are complete with respect to a natural class of ternary (...) relation models to show a similar result for the constant-free versions of the logic. In addition, we prove that the logics in question satisfy the variable sharing property, vindicating the claim that they really are relevant logics. (shrink)

Val Plumwood and Richard Sylvan argued from their joint paper The Semantics of First Degree Entailment and onward that the variable sharing property is but a mere consequence of a good entailment relation, indeed they viewed it as a mere negative test of adequacy of such a relation, the property itself being a rather philosophically barren concept. Such a relation is rather to be analyzed as a sufficiency relation free of any form of premise suppression. Suppression (...) of premises, therefore, gained center stage. Despite this, however, no serious attempt was ever made at analyzing the concept. This paper shows that their suggestions for how to understand it, either as the Anti-Suppression Principle or as the Joint Force Principle, turn out to yield properties strictly weaker than that of variable sharing. A suggestion for how to understand some of their use of the notion of suppression which clearly is not in line with these two mentioned principles is given, and their arguments to the effect that the Anderson and Belnap logics T, E and R are suppressive are shown to be both technically and philosophically wanting. Suppression-freedom, it is argued, cannot do the job Plumwood and Sylvan intended it to do. (shrink)

We introduce structural rules mingle, and investigatetheorem-equivalence, cut- eliminability, decidability, interpolabilityand variable sharing property for sequent calculi having the mingle.These results include new cut-elimination results for the extendedlogics: FLm (full Lambek logic with the mingle), GLm(Girard's linear logic with the mingle) and Lm (Lambek calculuswith restricted mingle).

Priest argued in Fusion and Confusion (Priest in Topoi 34(1):55–61, 2015a) for a new concept of logical consequence over the relevant logic B, one where premises my be “confused” together. This paper develops Priest’s idea. Whereas Priest uses a substructural proof calculus, this paper provides a Hilbert proof calculus for it. Using this it is shown that Priest’s consequence relation is weaker than the standard Hilbert consequence relation for B, but strictly stronger than Anderson and Belnap’s original relevant notion of (...) consequence. Unlike the latter, however, Priest’s consequence relation does not satisfy a variant of the variable sharing property. This paper shows that how it can be modified so as to do so. Priest’s consequence relation turns out to be surprisingly weak in some respects. The prospects of strengthening it is raised and discussed in a broader philosophical context. (shrink)

The computer is one of the most complex artifacts ever built. Given its complexity, it can be described from many different points of view. The aim of this paper is to investigate the representational structure and multifunctionality of a particular subset of computers, namely personal devices from a user-centred perspective. The paper also discusses the concept of “cognitive task”, as recently employed in some definitions of cognitive artifacts, and investigates the metaphysical properties of such artifacts. From a representational point of (...) view, the article introduces the concepts of artifactual meta-representation and of semi-transparency, two features that personal devices share with some cognitive and non-cognitive artifacts. Recognising the meta-representational nature of personal devices and of other cognitive artifacts, thus overcoming semi-transparency, is important for the understanding of why different artifacts offer us different cognitive affordances as well as different cognitive advantages. In this sense, it is not simply a theoretical achievement, but has some important practical consequences. In our highly technological world we can use different kinds of computers and artifacts for solving the same tasks, and we need to understand why some artifacts are better suited for some tasks than others. The ultimate characterisation of personal devices that emerges from this work is that of a sort of super-artifact. This special status is given to personal devices because of their distinctive features. They are in fact intrinsically multifunctional and meta-representational artifacts, with extremely variable structures. As super-artifacts, personal devices are characterised by macro-functionality and can be easily used as both cognitive artifacts and tools for other functions, depending on the kind of representations they instantiate. (shrink)

A situation, in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A (point-valued) solution for TU-games assigns a payoff distribution to every TU-game. In this article we discuss a class of equal surplus sharing solutions consisting of all convex combinations of the CIS-value, the ENSC-value and the equal division solution. We provide several characterizations of this class of solutions on variable (...) and fixed player set. Specifications of several properties characterize specific solutions in this class. (shrink)

We show that the elimination rule for the multiplicative (or intensional) conjunction $\wedge$ is admissible in many important multiplicative substructural logics. These include LL m (the multiplicative fragment of Linear Logic) and RMI m (the system obtained from LL m by adding the contraction axiom and its converse, the mingle axiom.) An exception is R m (the intensional fragment of the relevance logic R, which is LL m together with the contraction axiom). Let SLL m and SR m be, respectively, (...) the systems which are obtained from LL m and R m by adding this rule as a new rule of inference. The set of theorems of SR m is a proper extension of that of R m , but a proper subset of the set of theorems of RMI m . Hence it still has the variable-sharing property. SR m has also the interesting property that classical logic has a strong translation into it. We next introduce general algebraic structures, called strong multiplicative structures, and prove strong soundness and completeness of SLL m relative to them. We show that in the framework of these structures, the addition of the weakening axiom to SLL m corresponds to the condition that there will be exactly one designated element, while the addition of the contraction axiom corresponds to the condition that there will be exactly one nondesignated element (in the first case we get the system BCK m , in the second - the system SR m ). Various other systems in which multiplicative conjunction functions as a true conjunction are studied, together with their algebraic counterparts. (shrink)

The Routley star, an involutive function between possible worlds or set-ups against which negation is evaluated, is a hallmark feature of Richard Sylvan and Val Plumwood's set-up semantics for the logic of first-degree entailment. Less frequently acknowledged is the weaker mate function described by Sylvan and his collaborators, which results from stripping the requirement of involutivity from the Routley star. Between the mate function and the Routley star, however, lies an broad field of intermediate semantical conditions characterizing an infinite number (...) of consequence relations closely related to first-degree entailment. In this paper, we consider the semantics and proof theory for deductive systems corresponding to set-up models in which the mate function is cyclical. We describe modifications to Anderson and Belnap's consecution calculus LE_fde2 that correspond to these constraints, for which we prove soundness and completeness with respect to the set-up semantics. Finally, we show that a number of familiar metalogical properties are coordinated with the parity of a mate function's period, including refined versions of the variable-sharing property and the property of gentle explosiveness. (shrink)

I presented a sub-classical relating logic based on a relating via an NL-inspired relating relation Rcss. The relation Rcss is motivated by the NL-phenomenon of phrasal (subsentential) coordination, exhibiting an important aspect of contents relating among the arguments of binary connectives. The resulting logic Lcss can be viewed as a relevance logic exhibiting a contents related relevance, stronger than the variable-sharing property of other relevance logics like R. Note that relating here is not “tailored” to justify some (...) predetermined logic; rather, the relating relation is independently justified, and induces a logic not previously investigated. (shrink)

Ackermann’s motivational spin on his theory of rigorous implication is analyzed and it is shown to contain en equivalent idea to Plumwood’s notion of suppression freedom. The formal properties these ideas back turn out to be properly weaker than Belnap’s variable sharing property, but it is shown that they can be strengthen in various ways. Some such strengthenings, it is shown, yield properties which are equivalent to Belnap’s, and thus provide for new ways of motivating Belnap’s fundamental (...) relevance principle. (shrink)

In this paper we elaborate a conception of entailment based on what we call the Ackermann principle, which explicates valid entailment through a logical connection between sentences depending on their informational content. We reconstruct Dunn’s informational semantics for entailment on the basis of Restall’s approach, with assertion and denial as two independent speech acts, by introducing the notion of a ‘position description’. We show how the machinery of position descriptions can effectively be used to define the positive and the negative (...) information carried by sentences of a given language and to present a formalized version of the Ackermann principle as an inclusion relationship between the informational contents of the conclusions and the premises of a valid entailment. Being so interpreted, the entailment relation exhibits certain properties, including the property of transitivity. Whereas properties such as Anderson and Belnap’s variable sharing property or Parry’s proscriptive principle are normally presented as imposing a relevance requirement on valid entailment, the suggested formalization of the Ackermann principle supports all of Gentzen’s structural rules, including weakening, a rule that is normally given up in sequent-style proof systems for relevance logics. In this way we propose an Ackermann-inspired explication of the nature of entailment as a relation between the informational contents of sentences. (shrink)

The two ``relevance'' criteria set out by Anderson and Belnap are discussed. It is argued that the motivation backing the variable sharing property is far weaker than it is commonly made out to be, and that the use-criterion does not distinguish between relevant logics such as E and R and ``irrelevant'' logics such as S4, intuitionistic and classical logic. In short, then, the paper argues that Anderson and Belnap's two criteria of relevance are both motivationally unsound, and (...) do not accomplish what they are commonly taken to accomplish. (shrink)

In this article, I consider the positive logic of Boolean groups (i.e. Abelian groups where every non-identity element has order 2), where these are taken as frames for an operational semantics à la Urquhart. I call this logic BG. It is shown that the logic over the smallest nontrivial Boolean group, taken as a frame, is identical to the positive fragment of a quasi-relevance logic that was developed by Robles and Méndez (an extension of this result where negation is included (...) is also discussed). It is proved that BG satisfies the variable sharing property and is Halldén complete, while failing to satisfy the disjunction property. Sound and complete subscripted tableaux are presented for BG. An axiomatization (in the positive language extended with fusion) is presented, which is sound with respect to BG and, with respect to a related ternary relational semantics, complete; the problem of identifying a complete axiomatization for BG itself is left open. Connections between BG and the quasi-relevance logic KR are also discussed. (shrink)

The present paper is a sequel to Robles et al. :349–374, 2020. https://doi.org/10.1007/s10849-019-09306-2). A class of implicative expansions of Kleene’s 3-valued logic functionally including Łukasiewicz’s logic Ł3 is defined. Several properties of this class and/or some of its subclasses are investigated. Properties contemplated include functional completeness for the 3-element set of truth-values, presence of natural conditionals, variable-sharing property and vsp-related properties.

A Bayesian network consists of two distinct parts: a directed acyclic graph (DAG or belief-network structure) and a set of parameters for the DAG. The DAG in a Bayesian network can be used to represent both causal hypotheses and sets of probability distributions. Under the causal interpretation, a DAG represents the causal relations in a given population with a set of vertices V when there is an edge from A to B if and only if A is a direct cause (...) of B relative to V. (We adopt the convention that sets of variables are capitalized and boldfaced, and individual variables are capitalized and italicized.) Under the statistical interpretation a DAG G can be taken to represent a set of all distributions all of which share a set of conditional independence relations that are entailed by satisfying a local directed Markov property (defined below). (shrink)

Concepts stand at the centre of human cognition. We use concepts in categorizing objects and events in the world, in reasoning and action, and in social interaction. It is therefore not surprising that the study of concepts constitutes a central area of research in philosophy and psychology, yet only recently have the two disciplines developed greater interaction. Recent experiments in psychology that test the role of concepts in categorizing and reasoning have found a great deal of variation, across individuals and (...) cultures, in categorization behaviour. Meanwhile, philosophers of language and mind have investigated the semantic properties of concepts, and how concepts are related to linguistic meaning and linguistic communication. A key motivation behind this was the idea that concepts must be shared across individuals and cultures. With the dawn of experimental philosophy, the proposal that the experimental data from psychology lacks relevance to semantics is increasingly difficult to defend. -/- This volume brings together leading psychologists and philosophers to advance the interdisciplinary debate on the role of concepts in categorizing and reasoning, the relationship between concepts and linguistic meaning and communication, the challenges conceptual variation poses to communication, and the social and political effects of conceptual change. (shrink)

This paper concerns the interface between relevant logics and recent developments in semantics for hyperintensional operators. In the latter area, the notion of topicality or aboutness has begun to play an explicit modeling role, with classes of models being studied which incorporate representations of topics, and of operations on topics. The idea is to use these topics in the evaluations of formulas including hyperintensional operators in order to explain why classically equivalent formulas may not be intersubstitutable in contexts using those (...) operators—though classically equivalent, if a pair of formulas can be interpreted to concern totally unrelated topics, then we should not be able to substitute one for the other in contexts which are sensitive to topics. Relevant logics, and the central relevance property of Variable Sharing, have been read as concerning something like topics in the past, and recently this angle on relevance has seen renewed interest. In this paper, I’ll develop and motivate a method for representing topics in the matrix models of logics, and apply this method to _R_ and its matrix models (given by De Morgan monoids) to argue that there is a clear semantic perspective on topicality according to which _R_ is topic-sensitive as a logic. (shrink)

We provide a sucient frame-theoretic condition for a super bi-intuitionistic logic to have Maksimova's variable separation property. We conclude that bi-intuitionistic logic enjoys the property. Furthermore, we offer an algebraic characterization of the super-bi-intuitionistic logics with Maksimova's property.

Distinctions have been proposed between systems of reasoning for centuries. This article distills properties shared by many of these distinctions and characterizes the resulting systems in light of recent findings and theoretical developments. One system is associative because its computations reflect similarity structure and relations of temporal contiguity. The other is "rule based" because it operates on symbolic structures that have logical content and variables and because its computations have the properties that are normally assigned to rules. The systems serve (...) complementary functions and can simultaneously generate different solutions to a reasoning problem. The rule-based system can suppress the associative system but not completely inhibit it. The article reviews evidence in favor of the distinction and its characterization. (shrink)

The conditional independence relations present in a data set usually admit multiple causal explanations — typically represented by directed graphs — which are Markov equivalent in that they entail the same conditional independence relations among the observed variables. Markov equivalence between directed acyclic graphs (DAGs) has been characterized in various ways, each of which has been found useful for certain purposes. In particular, Chickering’s transformational characterization is useful in deriving properties shared by Markov equivalent DAGs, and, with certain generalization, is (...) needed to justify a search procedure over Markov equivalence classes, known as the GES algorithm. Markov equivalence between DAGs with latent variables has also been characterized, in the spirit of Verma and Pearl (1990), via maximal ancestral graphs (MAGs). The latter can represent the observable conditional independence relations as well as some causal features of DAG models with latent variables. However, no characterization of Markov equivalent MAGs is yet available that is analogous to the transformational characterization for Markov equivalent DAGs. The main contribution of the current paper is to establish such a characterization for directed MAGs, which we expect will have similar uses as Chickering’s characterization does for DAGs. (shrink)

We examine the set of formula-to-formula valid inferences of Classical Logic, where the premise and the conclusion share at least a propositional variable in common. We review the fact, already proved in the literature, that such a system is identical to the first-degree entailment fragment of R. Epstein's Relatedness Logic, and that it is a non-transitive logic of the sort investigated by S. Frankowski and others. Furthermore, we provide a semantics and a calculus for this logic. The semantics is (...) defined in terms of a \-matrix built on top of a 5-valued extension of the 3-element weak Kleene algebra, whereas the calculus is defined in terms of a Gentzen-style sequent system where the left and right negation rules are subject to linguistic constraints. (shrink)

In this systematic review, we aim to describe the association between temporal lobe epilepsy and sleep, with bidirectional links in mechanisms and therapeutic aspects. Sleep stages may variably impact seizure occurrence, secondary generalization and the development, frequency and distribution of interictal epileptiform discharges. Conversely, epilepsy affects sleep micro- and macroarchitecture. TLE, the most frequent form of drug resistant epilepsy, shares an enduring relationship with sleep, with some intriguing potential mechanisms specific to anatomic localization, linking the two. Sleep characteristics of TLE (...) may also inform localizing properties in persons with DRE, since seizures arising from the temporal lobe seem to be more common during wakefulness, compared to seizures of extratemporal origin. Polysomnographic studies indicate that persons with TLE may experience excessive daytime somnolence, disrupted sleep architecture, increased wake after sleep onset, frequent shifts in sleep stages, lower sleep efficiency, decreased rapid eye movement sleep, and possibly, increased incidence of sleep apnea. Limited literature suggests that effective epilepsy surgery may remedy many of these objective and subjective sleep-related concerns, via multipronged effects, apart from reduced seizure frequency. Additionally, sleep abnormalities also seem to influence memory, language and cognitive-executive function in both medically controlled and refractory TLE. Another aspect of the relationship pertains to anti-seizure medications, which may contribute significantly to sleep characteristics and abnormalities in persons with TLE. Literature focused on specific aspects of TLE and sleep is limited, and heterogeneous. Future investigations are essential to understand the pathogenetic mechanisms linking sleep abnormalities on epilepsy outcomes in the important sub-population of TLE. (shrink)

I argue that the study of variability rather than invariance should head the reading research agenda, and that strong claims of orthographic are unwarranted. I also expand briefly on Frost's assertion that an efficient orthography must represent sound and meaning, by considering writing systems as dual-purpose devices that must provide decipherability for novice readers and automatizability for the expert.

Why was Hensen unsuccesful in the quantification of ecological sampling? No aspect of plankton research itself seems to have hindered quantification; both collecting methods and taxonomy were sufficiently advanced. The reason is probably that at the time he began sampling, Hensen had to devise his own statistical methods for expressing the reproducibility and validity of samples. Hensen might have succeeded in this if he had overcome prevalent nineteenth-century attitudes toward randomness.The statistical literature of medicine and physics with which Hensen was (...) probably familiar gave methods for expressing reproducibility and for comparing differences between means of different sets of observations. For example, a student of Poisson writing on medical statistics advocated using Poisson's limit (standard error 2√2) to test the difference between two means56. Other authors suggested that differences between means were most meaningful if very large numbers of observations were used.57 In his laboratory subsampling, Hensen used the propable error as a limit about means. In this and other ways, he seems most indebted to the physicist Ernst Abbe for statistical methods.58 However, all the methodology available to Hensen had been developed for situations in which errors are a property of the measurement or sampling process, and not of the phenomena themselves. The available methods for measuring reproducibility were based on the assumption that differences from the average were small and that they tended to accumulate about the mean in a bell-shaped pattern. Hensen constantly reinvestigated the distribution of plankton numbers about the average using a different method each time. Westergaard points out that medical statisticians did not make such investigations with their biological data.59To a considerable extent, biological sampling problems forced development of theory because samples afforded the only information on a pattern in water or soil which could not be directly observed. The sampling methods of Laplace and the late nineteenth-century government statisticians contrasted strongly with Hensen's because, either through subjective knowledge of the population sampled or through censuses, they attempted to choose representative or typical samples.60 The high reproducibility and validity of representative sampling is attained by knowing more about a population than a biologist can ordinarily know. The uncertain reproducibility and validity of biological sampling spurred the development of formal sampling theory.A formal sampling theory developed only after change in the general intellectual attitude toward randomness, which was reflected in nineteenth-century statistics.61 The ninteenth-century attitude that randomness is not part of nature changed in the twentieth century to a view of randomness as a property of nature.62 The physicist's incorporation of randomness into physical models in response to this intellectual change late in the nineteenth-century is discussed by Bork.63 In biology, the change was initiated by the attention Darwin focused on morphological variation. The English biometricians — Francis Galton and W. F. R. Weldon, for example — were prominent in developing methods for the analysis of biological variation.64 Most pertinent to the development of sampling theory was Karl Pearson's use of frequency distributions as models of biological variation. In ecology, quantification was brought about by Ronald Fisher more than by anyone else; he incorporated randomness into sampling plans and built upon the methods developed earlier for analysis of individual variation. Fisher's use of random sampling allowed comparison between the sample collections and the collections expected from a model population of known patterning (calculated with a frequency distribution). This is a much more efficient method of determining the validity of a sample than Hensen's comparison of collections with a model uniform collection. Intellectual background and accumulated biological information caused Fisher to find variability where Hensen had seen uniformity.In summary, Victor Hensen became interested in fisheries research because of the economic importance of fishing to Germany. Hensen had considerable understanding of the prerequisites for valid sampling, but the value of his quantitative approach was limited by the general preconceptions shared by most nineteenth-century biologists. Through Hensen's efforts many other biologists were stimulated to undertake quantitative samples, even though the statistical methods for analyzing variation among populations developed only after methods for analyzing variation among individuals had been developed. *** DIRECT SUPPORT *** A8402011 00003. (shrink)

The current implementation of the Neo-Darwinian model of evolution typically assumes that the set of possible phenotypes is organized into a highly symmetric and regular space. Most conveniently, a Euclidean vector space is used, representing phenotypic properties by real-valued variables. Computational work on the biophysical genotype-phenotype model of RNA folding, however, suggests a rather different picture. If phenotypes are organized according to genetic accessibility, the resulting space lacks a metric and can be formalized only in terms of a relatively unfamiliar (...) structure. Patterns of phenotypic evolution—such as punctuation, irreversibility, and modularity—result naturally from the properties of the genotype-phenotype map, which, given the genetic accessibility structure, define accessibility in the phenotype space. The classical framework, however, addresses these patterns exclusively in terms of natural selection on suitably constructed fitness landscapes. Recent work has extended the explanatory level for phenotypic evolution from fitness considerations alone to include the topological structure of phenotype space as induced by the genotype-phenotype map. Lewontin’s notion of “quasi-independence” of characters can also be formalized in topological terms: it corresponds to the assumption that a region of the phenotype space is represented by a product space of orthogonal factors. In this picture, each character corresponds to a factor of a region of the phenotype space. We consider any region of the phenotype space that has a given factorization as a “type”, i.e., as a set of phenotypes that share the same set of phenotypic characters. Thus, a theory of character identity can be developed that is based on the correspondence of local factors in different regions of the phenotype space. (shrink)

What precisely are fragments of classical first-order logic showing “modal” behaviour? Perhaps the most influential answer is that of Gabbay 1981, which identifies them with so-called “finite-variable fragments”, using only some fixed finite number of variables (free or bound). This view-point has been endorsed by many authors (cf. van Benthem 1991). We will investigate these fragments, and find that, illuminating and interesting though they are, they lack the required nice behaviour in our sense. (Several new negative results support this (...) claim.) As a counterproposal, then, we define a large fragment of predicate logic characterized by its use of only bounded quantification. This so-called guarded fragment enjoys the above nice properties, including decidability, through an effectively bounded finite model property. (These are new results, obtained by generalizing notions and techniques from modal logic.) Moreover, its own internal finite variable hierarchy turns out to work well. Finally, we shall make another move. The above analogy works both ways. Modal operators are like quantifiers, but quantifiers are also like modal operators. This observation inspires a generalized semantics for first-order predicate logic with accessibility constraints on available assignments (cf. N´emeti 1986, 1992) which moves the earlier quantifier restrictions into the semantics. This provides a fresh look at the landscape of possible predicate logics, including candidates sharing various desirable features with basic modal logic – in particular, its decidability. (shrink)

We extend the notion of absolute convergence for real series in several variables to a notion of convergence for series in a power series field ℝ((t Γ)) with coefficients in ℝ. Subsequently, we define a natural notion of analytic function at a point of ℝ((t Γ))m. Then, given a real function f analytic on a open box I of ℝ m , we extend f to a function f ★ which is analytic on a subset of ℝ((t Γ)) m containing (...) I. We prove that the functions f ★ share with real analytic functions certain basic properties: they are , they have usual Taylor development, they satisfy the inverse function theorem and the implicit function theorem. (shrink)

Fluted Logic is essentially first-order predicate logic deprived of variables. The lack of variables results in reduced expressiveness. Nevertheless, many logical problems that can be stated in natural language, such as the famous Schubert's Steamroller, can be rendered in fluted logic. Further evidence of the expressiveness of fluted logic is its close relation to description logics. Already it has been shown that fluted logic is decidable and has the finite-model property. This paper shows that fluted logic has the exponential-model (...) property and that deciding satisfiability is NEXPTIME-complete. It is shown further that fluted logic is 'nice, that is, it shares with first-order predicate logic the interpolation property and model preservation properties. (shrink)

Few would disagree that P. F. Strawson and W. V. O. Quine have been the leading figures in Anglo-American philosophy during the second half of the twentieth century. This book brings together a number of Strawson’s widely-scattered previously-published essays from the 1970s, 1980s, and 1990s. The unity of the collection is partly provided by the internal connectedness of the essays to Strawson’s most important books Individuals, The Bounds of Sense, Logico-Linguistic Papers, and Subject and Predicate in Grammar and Logic. But (...) its unity principally lies in Strawson’s consistent and vigorous opposition to Quine’s extreme extensionalism. The extensionalist says that the meanings of terms and sentences in natural languages or logical systems are strictly determined by the objects they refer to; and the Quinean extensionalist also says that those objects are ultimately whatever the natural sciences tell us they are. The intensionalist, by contrast, says that meanings in natural language and logic are underdetermined by the functions of reference and have irreducible, autonomous structures that include primitive features of generality and modality; and the Strawsonian intensionalist says that those irreducible, autonomous structures are grounded in the person-oriented world of ordinary speech-transactions and everyday common sense. In the Introduction, Strawson helpfully divides the essays into seven groups or clusters: two on identity and universals; two on quantification and properties; three on singular reference and beliefreports; two on logical form; one on epistemic modality; two on pragmatics; and four on Kant. The essays on Kant are primarily exegeticalcritical, but also have a deeper import. For Strawson’s metaphysical commonsensism and personalism can be fairly neatly derived from Kantian metaphysics by logically detaching Kant’s plausible conception of “empirical realism” from his questionable doctrine of “transcendental idealism”, and by similarly detaching Kant’s plausible conception of a self-conscious embodied empirical subject and her a priori cognitive and practical capacities from his questionable conception of a noumenal self. It is of course impossible in a very short review even to summarize all sixteen essays, far less to explicate or criticize them. So to maximize available resources I will concentrate the rest of my remarks on what seems to me to be the most important paper. In “Logical Form and Logical Constants”, Strawson addresses a fundamental and lingering problem in the philosophy of logic: How precisely to define the logical constants and to justify their introduction into a logical theory? All logicians agree that logical constants are just those terms in a formal or natural language which hold their meanings fixed under the variable interpretations of all other terms, which enter essentially into logical truths and deductions, and which are “topic-neutral”—indifferent to all special subject-matters. But these notions do not get us very far, since the meaning of any term can be held rigidly and topic-neutrally fixed over a language and also held to enter essentially into logical truths and deductions, by sheer stipulation. Strawson’s approach to solving the problem has two basic steps. First, he joins a line of thought shared by Kant, Boole, and early Wittgenstein: “[l]ogic reveals the general essence of all thought and all language”. Secondly, he borrows and exploits Wittgenstein’s idea that all the logical constants are packed into the general form of a proposition, which is simply “this is how things are.” This leads to the proposal that we can “think of standard logic as something in principle excogitatable... by pure reflection on the general nature of statement, on what is the least that is necessarily involved in the making of empirical informative statements”. Such a line of reasoning— rather like Kant’s discovery of his “table of judgments” in the first Critique —runs backward from the notion of an empirical statement to the root logical notions of general term and singular term, of compatibility and incompatibility, and of “identifiable linguistic forms or devices with conventional forces or meaning” ; and from there by gradual steps to the notions of contradiction and entailment, the truth-functions, logical truth, first-order quantification, and so forth. I have a worry about this way of excogitating logic, however. While it neatly accounts for standard logic, I cannot see how it will be able to account for nonstandard logic—whether in the form of conservative extensions of standard logic or in the form of deviant logics. In other words, the starting point for logical reflection must be something more comprehensive than the empirical statement. Now the notion of an analytic a priori statement seems like the obvious candidate: no system, standard or nonstandard, will wholly lack logical laws or logical truths. If so, then Strawson’s disinclination to deploy the notion of analyticity directly may be a concession to Quine’s attack on the analytic-synthetic distinction. On this pivotal issue, in fact, Strawson’s intensionalism has lost out to Quine’s extensionalism—the Grice-Strawson reply to “Two Dogmas of Empiricism” from ordinary-language considerations has not generally prevailed. But we are very fortunate that Strawson has been both willing and so brilliantly able to resist the Quinean juggernaut for five decades.—Robert Hanna, University of Colorado at Boulder. (shrink)