The standard account of modal expressions in natural language analyzes them as quantifiers over a set of possible worlds determined by the evaluation world and an accessibility relation. A number of authors have recently argued for an alternative account according to which modals are analyzed as quantifying over a domain of possible worlds that is specified directly in the points of evaluation. But the new approach only handles the data motivating it if it is supplemented with a non-standard account of (...) attitude verbs and conditionals. It can be shown the the relational account handles the same data equally well if it too is supplemented with a non-standard account of such expressions. (shrink)

In this paper we present a characterization of hyper-connexivity by means of a relating semantics for Boolean connexive logics. We also show that the minimal Boolean connexive logic is Abelardian, strongly consistent, Kapsner strong and antiparadox. We give an example showing that the minimal Boolean connexive logic is not simplificative. This shows that the minimal Boolean connexive logic is not totally connexive.

We show that the relational semantics of the Lambek calculus, both nonassociative and associative, is also sound and complete for its extension with classical propositional logic. Then, using filtrations, we obtain the finite model property for the nonassociative Lambek calculus extended with classical propositional logic.

Six interesting variants of the logics BN4 and E4—which can be considered as the 4-valued logics of the relevant conditional and entailment, respectively—were previously developed in the literature. All these systems are related to the family of relevant logics and contain Routley and Meyer's basic logic B, which is well-known to be specifically associated with the ternary relational semantics. The aim of this paper is to develop reduced general Routley-Meyer semantics for them. Strong soundness and completeness theorems (...) are proved for each one of the logics. (shrink)

Nonclassical logics have played an increasing role in recent years in disciplines ranging from mathematics and computer science to linguistics and philosophy. _Generalized Galois Logics_ develops a uniform framework of relational semantics to mediate between logical calculi and their semantics through algebra. This volume addresses normal modal logics such as K and S5, and substructural logics, including relevance logics, linear logic, and Lambek calculi. The authors also treat less-familiar and new logical systems with equal deftness.

The logic BN4 was defined by R.T. Brady in 1982. It can be considered as the 4-valued logic of the relevant conditional. E4 is a variant of BN4 that can be considered as the 4-valued logic of entailment. The aim of this paper is to define reduced general Routley-Meyer semantics for BN4 and E4. It is proved that BN4 and E4 are strongly sound and complete w.r.t. their respective semantics.

In this paper we give relational semantics and an accompanying relational proof theory for full Lambek calculus (a sequent calculus which we denote by FL). We start with the Kripke semantics for FL as discussed in [11] and develop a second Kripke-style semantics, RelKripke semantics, as a bridge to relational semantics. The RelKripke semantics consists of a set with two distinguished elements, two ternary relations and a list of conditions on the (...) relations. It is accompanied by a Kripke-style valuation system analogous to that in [11]. Soundness and completeness theorems with respect to FL hold for RelKripke models. Then, in the spirit of the work of Orlowska [14], [15], and Buszkowski and Orlowska [3], we develop relational logic RFL. The adjective relational is used to emphasize the fact that RFL has a semantics wherein formulas are interpreted as relations. We prove that a sequent Γ → α in FL is provable if and only if a translation, t( $\gamma_1 \bullet \cdots \bullet \gamma_n \supset \alpha)\varepsilon \upsilon u$ , has a cut-complete fundamental proof tree. This result is constructive: that is, if a cut-complete proof tree for $t(\gamma_1 \bullet \cdots \bullet \gamma_n \supset \alpha)\varepsilon \upsilon u$ is not fundamental, we can use the failed proof search to build a relational countermodel for $t(\gamma_1 \bullet \cdots \bullet \gamma_n \supset \alpha)\varepsilon \upsilon u$ and from this, build a RelKripke countermodel for $\gamma_1 \bullet \cdots \bullet \gamma_n \supset \alpha$ . These results allow us to add FL, the basic substructural logic, to the list of those logies of importance in computer science with a relational proof theory. (shrink)

This paper deals with a collection of concerns that, over a period of time, led the author away from the Routley–Meyer semantics, and towards proof- theoretic approaches to relevant logics, and indeed to the weak relevant logic MC of meaning containment.

Kleene algebras and action logic were proposed to be solutions to the finite axiomatization problem of the algebra of regular sets (of strings). They are treated here as nonclassical logics—with Hilbert-style axiomatizations and semantics. We also provide intuitive accounts in terms of information states of the semantics which provide further insights into the formalisms. The three types of "Kripke-style'' semantics which we define develop insights from gaggle theory, and from our four-valued and generalized Kripke semantics for (...) the minimal substructural logic. Soundness and completeness are proven each time. (shrink)

The aim of this paper is to explore the advantages deriving from the application of relating semantics in epistemic logic. As a first step, I will discuss two versions of relating semantics and how they can be differently exploited for studying modal and epistemic operators. Next, I consider several standard frameworks which are suitable for modelling knowledge and related notions, in both their implicit and their explicit form and present a simple strategy by virtue of which they can (...) be associated with intuitive systems of relating logic. As a final step, I will focus on the logic of knowledge based on justification logic and show how relating semantics helps us to provide an elegant solution to some problems related to the standard interpretation of the explicit epistemic operators. (shrink)

This book presents a study of meaning relations, linking the philosophical tradition of conceptual analysis with recent theories and methodologies in cognitive semantics. Its main concern is the extent to which analyzing meaning relations between cognate words reveal the infrastructure of the actual and mental lexicon, assuming that language mirrors thought. Sovran aims to elucidate their infrastructure and the metaphorical and perceptual models that constitute abstract concepts, dealing finally with the role of abstraction in poetic metaphors. Overall, this volume (...) addresses major contemporary issues in the philosophy of language and theoretical semantics. (shrink)

Routley-Meyer Ternary Relational Semantics for Intuitionistic-type Negations examines how to introduce intuitionistic-type negations into RM-semantics. RM-semantics is highly malleable and capable of modeling families of logics which are very different from each other. This semantics was introduced in the early 1970s, and was devised for interpreting relevance logics. In RM-semantics, negation is interpreted by means of the Routley operator, which has been almost exclusively used for modeling De Morgan negations. This book provides research on (...) particular features of intuitionistic-type of negations in RM-semantics, while also defining the basic systems and many of their extensions by using models with or without a set of designated points. (shrink)

The problem of whether Lambek Calculus is complete with respect to (w.r.t.) relational semantics, has been raised several times, cf. van Benthem (1989a) and van Benthem (1991). In this paper, we show that the answer is in the affirmative. More precisely, we will prove that that version of the Lambek Calculus which does not use the empty sequence is strongly complete w.r.t. those relational Kripke-models where the set of possible worlds,W, is a transitive binary relation, while that (...) version of the Lambek Calculus where we admit the empty sequence as the antecedent of a sequent is strongly complete w.r.t. those relational models whereW=U×U for some setU. We will also look into extendability of this completeness result to various fragments of Girard's Linear Logic as suggested in van Benthem (1991), p. 235, and investigate the connection between the Lambek Calculus and language models. (shrink)

Here, we discuss historical, philosophical and technical problems associated with relating logic and relating semantics. To do so, we proceed in three steps. First, Section 1 is devoted to providing an introduction to both relating logic and relating semantics. Second, we address the history of relating semantics and some of the main research directions and their philosophical applications. Third, we discuss some technical problems related to relating semantics, particularly whether the direct incorporation of the relation into (...) the language of relating logic is needed. The starting point for our considerations presented here is the 1st Workshop On Relating Logic and the selected papers for this issue. (shrink)

The contribution of this paper lies with providing a systematically specified and intuitive interpretation pattern and delineating a class of relational structures and models providing a natural interpretation of logical operators on an underlying propositional calculus of Positive Lattice Logic and subsequently proving a generic completeness theorem for the related class of logics, sometimes collectively referred to as Generalized Galois Logics.

A number of significant contributions in the last four decades show that non-normal modal logics can be fruitfully employed in several applied fields. Well-known domains are epistemic logic, deontic logic, and systems capturing different aspects of action and agency such as the modal logic of agency, concurrent propositional dynamic logic, game logic, and coalition logic. Semantics for such logics are traditionally based on neighbourhood models. However, other model-theoretic semantics can be used for this purpose. Here, we systematically study (...) multi-relational structures, whose investigation is still relatively underdeveloped. After a brief introduction to two different versions of multi-relational semantics – which we call strong and weak multi-relational semantics – we proceed to study several modal schemata. Special attention is paid to the schemata CON and D. Finally we offer completeness proofs for several systems using both strong and weak semantic tools: The proofs thus cover both classical system.. (shrink)

We present cut-free labelled sequent calculi for a central formalism in logics of agency: STIT logics with temporal operators. These include sequent systems for Ldm , Tstit and Xstit. All calculi presented possess essential structural properties such as contraction- and cut-admissibility. The labelled calculi G3Ldm and G3Tstit are shown sound and complete relative to irreflexive temporal frames. Additionally, we extend current results by showing that also Xstit can be characterized through relational frames, omitting the use of BT+AC frames.

Implicational tonoid logics and their relational semantics have been introduced by Yang and Dunn. This paper extends this investigation to implicational partial Galois logics. For this, we first define some implicational partial gaggle logics as special kinds of implicational tonoid logics called “implicational partial Galois logics.” Next, we provide Routley–Meyer-style relational semantics for finitary those logics.

In the chapter on quantum logic in Volume 6 of Handbook of Philosophical Logic, Dalla Chiara and Giuntini make an interesting observation that there is a unified relational semantics underlying both the {¬,∧}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{ {\lnot }, {\wedge } \}$$\end{document}-fragment of intuitionistic logic and ortho-logic. In this paper, we contribute to a systematic investigation of this relational semantics by providing an axiomatization of its logic.

Here, we discuss logical, philosophical and technical problems associated to relating logic and relating semantics. To do so, we proceed in three steps. The first step is devoted to providing an introduction to both relating logic and relating semantics. We discuss this problem on the example of different languages. Second, we address some of the main research directions and their philosophical applications to non-classical logics, particularly to connexive logics. Third, we discuss some technical problems related to relating (...) class='Hi'>semantics, and its application to philosophy of science, language and pragmatics. (shrink)

Minimal Negation is defined within the basic positive relevance logic in the relational ternary semantics: B+. Thus, by defining a number of subminimal negations in the B+ context, principles of weak negation are shown to be isolable. Complete ternary semantics are offered for minimal negation in B+. Certain forms of reductio are conjectured to be undefinable (in ternary frames) without extending the positive logic. Complete semantics for such kinds of reductio in a properly extended positive logic (...) are offered. (shrink)

Analytic reductivism in metaethics has long been out of philosophical vogue. In Confusion of Tongues: A Theory of Normativity (2014), Stephen Finlay tries to resuscitate it by developing an analytic metaethical reductive naturalistic semantics for ‘good.’ He argues that an end-relational semantics is the simplest account that can explain all of the data concerning the term, and hence the most plausible theory of it. I argue that there are several assumptions that a reductive naturalist would need to (...) make about contextual parameter completion to derive reductive naturalism from an end-relational semantics—assumptions that nonnaturalists might forcefully resist. I also argue for the claim that an end-relational semantics could provide surprising resources for nonnaturalists to address semantic worries about their views—the upshot of which paints the way for a new and sophisticated nonnaturalism about the semantics of moral discourse. Nonnaturalists have long suspected that they need not worry about semantics and this paper lends support to that suspicion. (shrink)

Recently M. Szabolcs [12] has shown that many substructural logics including Lambek CalculusL are complete with respect to relativized Relational Semantics. The current paper proves that it is sufficient forL to consider a relativization to the relation x dividesy in some fixed semigroupG.

This paper presents an algebraic approach of some many-valued generalizations of modal logic. The starting point is the definition of the [0, 1]-valued Kripke models, where [0, 1] denotes the well known MV-algebra. Two types of structures are used to define validity of formulas: the class of frames and the class of Ł n -valued frames. The latter structures are frames in which we specify in each world u the set (a subalgebra of Ł n ) of the allowed truth (...) values of the formulas in u. We apply and develop algebraic tools (namely, canonical and strong canonical extensions) to generate complete modal n + 1-valued logics and we obtain many-valued counterparts of Shalqvist canonicity result. (shrink)

In this paper, we apply relating semantics to the widely discussed problem of free choice between permitted actions or situations in normative systems. Leaving aside contexts in which the free choice principle is obviously unacceptable or uncontroversially valid, we concentrate on free choice for explicit permissions. In order to construct a formal representation of explicit permissions, we introduce a special constant, $\texttt {permit}$, which is analogous to the constant $\texttt {violation}$ used in the Andersonian–Kangerian approach to deontic logic with (...) respect to prohibition and obligation. Consequently, we define a permission operator on the basis of the $\texttt {permit}$ constant and a relation of legitimization. The general idea is that $P \varphi $ is true if and only if $\texttt {permit}$ is true, which means that a permission is actually issued and $\varphi $ is legitimized by $\texttt {permit}$. The intuitive notion of legitimization is formally represented by an operator of relating implication: a non-classical implication that is semantically defined by adding a constraint to the classical meaning of implication to the effect that arguments are related by a special relation. The properties of this relation are based on an informal, intuitive meaning of legitimization and determine the properties of the permission operator. We show that the resulting permission operator possesses the free choice property and avoids certain unwanted consequences that follow from alternative approaches. (shrink)

This paper combines two classes of generalized logics, one of which is the class of weakly implicative logics introduced by Cintula and the other of which is the class of gaggle logics introduced by Dunn. For this purpose we introduce implicational tonoid logics. More precisely, we first define implicational tonoid logics in general and examine their relation to weakly implicative logics. We then provide algebraic semantics for implicational tonoid logics. Finally, we consider relational semantics, called Routley–Meyer–style (...) class='Hi'>semantics, for finitary those logics. (shrink)

We present a labelled version of Lambek Calculus without unit, and we use it to prove a completeness theorem for Lambek Calculus with respect to some relational semantics.

This book explores how some word meanings are paradigmatically related to each other, for example, as opposites or synonyms, and how they relate to the mental organization of our vocabularies. Traditional approaches claim that such relationships are part of our lexical knowledge (our "dictionary" of mentally stored words) but Lynne Murphy argues that lexical relationships actually constitute our "metalinguistic" knowledge. The book draws on a century of previous research, including word association experiments, child language, and the use of synonyms and (...) antonyms in text. (shrink)

In the paper we examine the problem of logical systems that are extensions of Classical Propositional Logic with new, intensional connectives of agency: monadic and dyadic _bringing it about that_. These systems are usually studied within the neighbourhood semantics. Here we propose a different strategy. We study all of the accepted laws and rules of logic of agency and define a translation of the agency operators into connectives interpreted in relating semantics. After this translation we can make a (...) reduction to more basic semantic properties that are required by the particular groups of laws and axioms. Finally, we define proper semantic structures and prove that they are complete with respect to all possible logical systems determined by the combinations of the axioms and rules. (shrink)

Modal logics with the binary operator Until are considered. It is shown that there exists a continuum of consistent U-logics without Kripke frames, and that each U-logic whose class of order does not have the finite frame property.

We present a semantic study of a family of modal intuitionistic linear systems, providing various logics with both an algebraic semantics and a relational semantics, to obtain completeness results. We call modality a unary operator on formulas which satisfies only one rale (regularity), and we consider any subsetW of a list of axioms which defines the exponential of course of linear logic. We define an algebraic semantics by interpreting the modality as a unary operation on an (...) IL-algebra. Then we introduce a relational semantics based on pretopologies with an additional binary relationr between information states. The interpretation of is defined in a suitable way, which differs from the traditional one in classical modal logic. We prove that such models provide a complete semantics for our minimal modal system, as well as, by requiring the suitable conditions onr (in the spirit of correspondence theory), for any of its extensions axiomatized by any subsetW as above. We also prove an embedding theorem for modal IL-algebras into complete ones and, after introducing the notion of general frame, we apply it to obtain a duality between general frames and modal IL-algebras. (shrink)

First the Branching Space-time and Branching Continuations mod-els are briefly presented. We compare their properties with the traditional definition of a Flow of Time from physics and we point out the difficulties of it in relativistic time. A solution of a Flow of Time in the given models is then proposed.

This is the first of a series of papers devoted to the thorough investigation of refinement based on an underlying partial relational model. In this paper we restrict attention to operation refinement. We explore four theories of refinement based on an underlying partial relation model for specifications, and we show that they are all equivalent. This, in particular, sheds some light on the relational completion operator due to Woodcock which underlies data refinement in, for example, the specification language (...) Z. It further leads to two simple alternative models which are also equivalent to the others. (shrink)

This article reports a study carried out in order to measure how semantic factors affect reductions in the difficulty of the Chinese Ring Puzzle (CRP) that involves removing five objects according to a recursive rule. We hypothesised that semantics would guide inferences about action decision making. The study involved a comparison of problem solving for two semantic isomorphic variants of the CRP ( fish and fleas ) with problem solving for the puzzle's classic variant (the Balls and Boxes problem; (...) Kotovsky learning involves generalising the relations within a coherent, interconnected whole that makes up the puzzle's rules. It seems that semantics make it easier for the puzzle's elements to be grouped together within coherent, meaningful wholes, which reduces relational complexity and facilitates problem solving. (shrink)

Probing semantic relations Exploration and identification in specialized texts Alain Auger and Caroline Barrière In recent years, several scientific ...

Research has independently highlighted the roles of semantic memory and associative abilities in creative thinking. However, it remains unclear how these two capacities relate to each other, nor ho...

When young children learn to use language, they start to use their hands in co‐verbal gesturing. There are, however, considerable differences between children, and it is not completely understood what these individual differences are due to. We studied how children at 4 years of age employ speech and iconic gestures to convey meaning in different kinds of spatial event descriptions, and how this relates to their cognitive abilities. Focusing on spontaneous illustrations of actions, we applied a semantic feature (SF) analysis (...) to characterize combinations of speech and gesture meaning and related them to the child's visual‐spatial abilities or abstract/concrete reasoning abilities (measured using the standardized SON‐R test). Results show that children with higher cognitive abilities convey significantly more meaning via gesture and less solely via speech. These findings suggest that young children's use of cospeech representational gesturing is positively related to their mental representation and reasoning abilities. (shrink)

We consider two systems of constructive modal logic which are computationally motivated. Their modalities admit several computational interpretations and are used to capture intensional features such as notions of computation, constraints, concurrency, etc. Both systems have so far been studied mainly from type-theoretic and category-theoretic perspectives, but Kripke models for similar systems were studied independently. Here we bring these threads together and prove duality results which show how to relate Kripke models to algebraic models and these in turn to the (...) appropriate categorical models for these logics. (shrink)