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Modern language models and vector-symbolic architectures show that vector-based models are capable of handling the compositional, structured, and symbolic properties required for human concepts. Vectors are also able to handle key phenomena from the psychology, including computation of features and similarities, reasoning about relations and analogies, and representation of theories. Language models show how vector representation of word semantics and sentences can interface between concepts and language, as seen in definitional theories of concepts or ad hoc concepts. The idea of Church encoding, from logic, allows us to understand how meaning can arise in vector-based or symbolic systems. By combining these recent computational results with classic findings in psychology, vector-based models provide a compelling account of human conceptual representation. For decades, cognitive scientists have debated what kind of representation might characterize human concepts. Whatever the format of the representation, it must allow for the computation of varied properties, including similarities, features, categories, definitions, and relations. It must also support the development of theories, ad hoc categories, and knowledge of procedures. Here, we discuss why vector-based representations provide a compelling account that can meet all these needs while being plausibly encoded into neural architectures. This view has become especially promising with recent advances in both large language models and vector symbolic architectures. These innovations show how vectors can handle many properties traditionally thought to be out of reach for neural models, including compositionality, definitions, structures, and symbolic computational processes. [ABSTRACT FROM AUTHOR]

Bruno Whittle (2019) has recently extended Kripke's semantical theory of truth to languages containing generalized quantifiers. There are reasons for axiomatizing semantical theories, and for regarding Halbach and Horsten's PKF as a good axiomatization of Kripke's. PKF is a theory in Partial Logic. The present paper complements Whittle's by showing how Partial Logic, and then PKF, may be extended to cover binary quantifiers meaning 'every', 'some', and 'most'. [ABSTRACT FROM AUTHOR]

Georg Henrik von Wright (1916–2003) started his studies in theoretical philosophy at the University of Helsinki in 1934. His teacher, Professor Eino Kaila (1890–1958), was an associate of the Vienna Circle who had changed the course of Finnish philosophy with his own version of logical empiricism. Under Kaila's supervision, von Wright wrote his early studies on probability and defended his doctoral thesis The Logical Problem of Induction in 1941. Von Wright met Ludwig Wittgenstein in Cambridge in 1939 and 1947 and eventually became his successor there in 1948–1951. Later, von Wright characterized these two philosophers as his "father figures": "Kaila had turned me into a logical positivist or empiricist. Wittgenstein, on the other hand, thoroughly eradicated this personality of mine." This article studies von Wright's changing relation to logical empiricism. The main sources include his correspondence with Kaila in 1937–1958 and his books Den logiska empirismen (in Swedish in 1943; in Finnish in 1945) and Logik, filosofi och språk (in Swedish in 1957, in Finnish in 1958). In his "Intellectual Autobiography" (1989), von Wright described the former book as "a farewell to the philosophy of my student years". Wittgenstein's influence can be seen in von Wright's denial of the unity of science and his cool cultural pessimism as expressed in his critical essays. But it is also evident that logic and exact thinking continued to be central tools and ingredients of his subsequent and highly appreciated work as an analytic philosopher. [ABSTRACT FROM AUTHOR]

Game comonads, introduced by Abramsky, Dawar and Wang and developed by Abramsky and Shah, give an interesting categorical semantics to some Spoiler-Duplicator games that are common in finite model theory. In particular they expose connections between one-sided and two-sided games, and parameters such as treewidth and treedepth and corresponding notions of decomposition. In the present paper, we expand the realm of game comonads to logics with generalised quantifiers. In particular, we introduce a comonad graded by two parameters n ≤ k such that isomorphisms in the resulting Kleisli category are exactly Duplicator winning strategies in Hella's n-bijection game with k pebbles. We define a one-sided version of this game which allows us to provide a categorical semantics for a number of logics with generalised quantifiers. We also give a novel notion of tree decomposition that emerges from the construction. [ABSTRACT FROM AUTHOR]

FDE , LP and |$\mathbf {K_{3}}$| are closely related to each other and admit of an intuitive informational interpretation. However, all these logics are co-NP complete, and so idealized models of how an agent can think. We address this issue by shifting to signed formulae, where the signs express imprecise values associated with two bipartitions of the corresponding set of standard values. We present proof systems whose operational rules are all linear and have only two structural branching rules that express a generalized Principle of Bivalence. Each of these systems leads to defining an infinite hierarchy of tractable approximations to the respective logic, in terms of the maximum number of allowed nested applications of the two branching rules. Further, each resulting hierarchy admits of an intuitive 5-valued non-deterministic semantics. [ABSTRACT FROM AUTHOR]

Subresiduated lattices were introduced during the decade of 1970 by Epstein and Horn as an algebraic counterpart of some logics with strong implication previously studied by Lewy and Hacking. These logics are examples of subintuitionistic logics, i.e. logics in the language of intuitionistic logic that are defined semantically by using Kripke models, in the same way as intuitionistic logic is defined, but without requiring of the models some of the properties required in the intuitionistic case. Also in relation with the study of subintuitionistic logics, Celani and Jansana get these algebras as the elements of a subvariety of that of weak Heyting algebras. Here, we study both the implicative and the implicative-infimum subreducts of subresiduated lattices. Besides, we propose a calculus whose equivalent algebraic semantics is given by these classes of algebras. Several expansions of these calculi are also studied together with some interesting properties of them. [ABSTRACT FROM AUTHOR]

Religious expressivism is the view that religious sentences, like 'God is all-loving' and 'God offers us the gift of salvation', are devoid of cognitive meaning. Such sentences are not truth-evaluable: they cannot be judged as true or false. In Religious Language , Michael Scott asked what explains the seeming logical behaviour of religious sentences if they are not truth-evaluable, as religious expressivists claim. In particular, religious expressivists need to explain (i) how a given religious sentence and its negation seem inconsistent and (ii) how religious sentences could figure in logically valid arguments. In this article, I develop a version of Weak Kleene semantics that could address these two 'logic' challenges. [ABSTRACT FROM AUTHOR]

The logic of bringing-it-about (BIAT) aims to capture a notion of agency in which actions are analysed in terms of their results: 'An agent does something' means that the agent brings it about that something takes place. Our starting point is the basic BIAT logic as introduced by Elgesem in the '90s: this logic contains only a modal operator to express BIAT statements by single agents. Several extensions have been proposed by Elgesem himself and others, notably with the capability operator, coalitions of agents and means-end BIAT statements (i.e. of the form 'the agent does B by doing A'). We first propose a variant of the neighbourhood semantics, called bi-neighbourhood semantics, for the basic BIAT logic and the mentioned extensions, in which a world is equipped by a set of pairs or neighbourhoods. Differently from the semantics defined in the literature, this reformulation is well suited for countermodel construction. We then introduce modular hypersequent calculi for all logics considered in this work. Our calculi enjoy the fundamental property of cut admissibility, from which it follows their completeness with respect to the axiomatization. Moreover, our calculi provide at the same time a decision procedure, as well as the first practical countermodel extraction procedure: from a single failed proof it is possible to build directly a finite countermodel of the formula under verification in the bi-neighbourhood semantics. By this last result, we obtain constructive proofs of the semantic completeness of the calculi and consequently of the finite model property for all logics. [ABSTRACT FROM AUTHOR]

This conversation elaborates on the latest work of the Paris-based writer, philosopher, translator, mathematician and pianist Andrei Vieru, where he maintains that human freedom is inseparable from the idea of closure. Vieru’s model is rooted in the topological semantics of modal logic and provides valuable epistemological insights for the broader community of scholars (death and grief scholars, social scientists, humanists) as well as for policymakers, civil social actors and, generally, for all existentially concerned individuals in times of eroding democracies and pressing global risks. In this dialogue conducted during 2023 in face-to-face sessions and via email exchanges between Paris and Bucharest, Vieru reflects on what is at stake philosophically, artistically and existentially when humans are confronted with the radical openness of possibilities brought by contemporary challenges like global crises and digital technologies. [ABSTRACT FROM AUTHOR]

The aim of this article is to show that, just as in recent years Cobreros, Egré, Ripley and van Rooij have provided a non-transitive counterpart of classical logic (i.e. one in which all classically acceptable inferences are valid but Cut and other metainferences are not), the same can be done for every Tarskian logic, with full generality. To establish this fact, a semantic approach is taken by showing that appropriate structures can be devised to characterize a non-transitive counterpart of every Tarskian logic, starting from the logical matrices that are usually taken to render them. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study a particular family of non-deterministic semantics for modal logics that has eight truth-values. These eight-valued semantics can be traced back to Omori and Skurt (2016), where a particular member of this family was used to characterize the normal modal logic K. The truth-values in these semantics convey information about a proposition's truth/falsity, whether the proposition is necessary/not necessary, and whether it is possible/not possible. Each of these triples is represented by a unique value. In this paper we will study which modal logics can be obtained by changing the interpretation of the □ modality, assuming that the interpretation of other connectives stays constant. We will show what axioms are responsible for a particular interpretations of □ . Furthermore, we will study subsets of these axioms. We show that some of the combinations of the axioms are equivalent to well-known modal axioms. We apply the level-valuation technique to all of the systems to regain the closure under the rule of necessitation. We also point out that some of the resulting logics are not sublogics of S5 and comment briefly on the corresponding frame conditions that are forced by these axioms. Ultimately, we sketch a proof of meta-completeness for all of these systems. [ABSTRACT FROM AUTHOR]

This study argues that many of the formalizations used in analyses employing the notion of logical scope fail to conform to natural language in important ways and lead to false predictions. This is due to the fact that they pursue the logic-driven goal of making the structure of logical arguments more transparent and mechanically calculable rather than the language-driven goal of accounting for how the linguistic signs used in an utterance and their configuration contribute to the conveying of the message being fashioned by the speaker. The focus of the study is on categories associated with the verb: tense, aspect, modality and negation. The conclusion suggests that very precise and rigid theories using logical scope relations may force the theorist to straitjacket the data so that they fit the theory, thereby obscuring rather than clarifying the nature of linguistic categories and their interactions. Informal analyses that hew closer to natural language's semantic reality can provide greater understanding of phenomena such as the purported non-negatability of must. Seeing this English modal's meaning as defined in opposition to real existence leads to the realization that it does not interact with negation the same way as the reality of the existence of the property of being necessary does. [ABSTRACT FROM AUTHOR]

Kettle logic is a colloquial term that describes an agent's advancement of inconsistent arguments in order to defeat a particular claim. Intuitively, a consistent subset of the advanced arguments should exist that is at least as successful at refuting the claim as the advancement of the set of inconsistent arguments. In this paper, we formalize this intuition and provide a formal analysis of kettle logic in abstract argumentation, a fundamental approach to computational argumentation, showing that all of the analysed abstract argumentation semantics (inference functions)—with the exception of naive semantics, which is considered a mere simplistic helper for the construction of other semantics—suffer from kettle logic. We also provide an approach to mitigating kettle logic under some circumstances. The key findings presented in this paper highlight that agents that apply the inference functions of abstract argumentation, are—similarly to humans—receptive to persuasion by agents who deliberately advance inconsistent and intuitively 'illogical' claims. As abstract argumentation can be considered one of the most basic models of computational argumentation, this raises the question to what extent and under what circumstances kettle logic-free argumentation can and should be enforced by computational means. [ABSTRACT FROM AUTHOR]

This paper introduces a logic language LCA as a model of one-dimensional d-state m-neighborhood cellular automata (CAs) with d, m ≥ 2. We first develop the syntax of LCA, and then semantics are given to LCA in the domain of all d-ary strings. It is shown that the finite CAs of any d and m are models of the proposed logic language under any boundary condition. Classical CAs, which are defined over an infinite lattice, are also shown to be models of LCA under two popular classes of configurations: finite and periodic. The proposed logical model further guides us to develop a new class of CAs, which we name homoasynchronous CAs, where a group of (nearby) cells with homogeneous configurations can be updated independently during evolution. [ABSTRACT FROM AUTHOR]

We describe a general approach to deriving linear-time logics for a wide variety of state-based, quantitative systems, by modelling the latter as coalgebras whose type incorporates both branching and linear behaviour. Concretely, we define logics whose syntax is determined by the type of linear behaviour, and whose domain of truth values is determined by the type of branching behaviour, and we provide two semantics for them: a step-wise semantics akin to that of standard coalgebraic logics, and a path-based semantics akin to that of standard linear-time logics. The former semantics is useful for model checking, whereas the latter is the more natural semantics, as it measures the extent with which qualitative properties hold along computation paths from a given state. Our main result is the equivalence of the two semantics. We also provide a semantic characterisation of a notion of logical distance induced by these logics. Instances of our logics support reasoning about the possibility, likelihood or minimal cost of exhibiting a given linear-time property. [ABSTRACT FROM AUTHOR]

We propose a simple imperative programming language, ERC, that features arbitrary real numbers as primitive data type, exactly. Equipped with a denotational semantics, ERC provides a formal programming language-theoretic foundation to the algorithmic processing of real numbers. In order to capture multi-valuedness, which is well-known to be essential to real number computation, we use a Plotkin powerdomain and make our programming language semantics computable and complete: all and only real functions computable in computable analysis can be realized in ERC. The base programming language supports real arithmetic as well as implicit limits; expansions support additional primitive operations (such as a user-defined exponential function). By restricting integers to Presburger arithmetic and real coercion to the ‘precision’ embedding Z ∋ p 7→ 2p ∈ R, we arrive at a first-order theory which we prove to be decidable and model-complete. Based on said logic as specification language for preconditions and postconditions, we extend Hoare logic to a sound (w.r.t. the denotational semantics) and expressive system for deriving correct total correctness specifications. Various examples demonstrate the practicality and convenience of our language and the extended Hoare logic. [ABSTRACT FROM AUTHOR]

Formal, mathematically rigorous programming language semantics are the essential prerequisite for the design of logics and calculi that permit automated reasoning about concurrent programs. We propose a novel modular semantics designed to align smoothly with program logics used in deductive verification and formal specification of concurrent programs. Our semantics separates local evaluation of expressions and statements performed in an abstract, symbolic environment from their composition into global computations, at which point they are concretised. This makes incremental addition of new language concepts possible, without the need to revise the framework. The basis is a generalisation of the notion of a program trace as a sequence of evolving states that we enrich with event descriptors and trailing continuation markers. This allows to postpone scheduling constraints from the level of local evaluation to the global composition stage, where well-formedness predicates over the event structure declaratively characterise a wide range of concurrency models. We also illustrate how a sound program logic and calculus can be defined for this semantics. [ABSTRACT FROM AUTHOR]

Two semantic paradoxes, the Liar and Curry's paradox, are analysed using a newly developed conception of procedural semantics (semantics according to which the truth of propositions is determined algorithmically), whose main characteristic is its departure from methodological realism. Rather than determining pre-existing facts, procedures are constitutive of them. Of this semantics, two versions are considered: closed (where the halting of procedures is presumed) and open (without this presumption). To this end, a procedural approach to deductive reasoning is developed, based on the idea of simulation. As is shown, closed semantics supports classical logic, but cannot in any straightforward way accommodate the concept of truth. In open semantics, where paradoxical propositions naturally 'belong', they cease to be paradoxical; yet, it is concluded that the natural choice--for logicians and common people alike--is to stick to closed semantics, pragmatically circumventing problematic utterances. [ABSTRACT FROM AUTHOR]

We introduce and analyze a new axiomatic theory $\mathsf {CD}$ of truth. The primitive truth predicate can be applied to sentences containing the truth predicate. The theory is thoroughly classical in the sense that $\mathsf {CD}$ is not only formulated in classical logic, but that the axiomatized notion of truth itself is classical: The truth predicate commutes with all quantifiers and connectives, and thus the theory proves that there are no truth value gaps or gluts. To avoid inconsistency, the instances of the T-schema are restricted to determinate sentences. Determinateness is introduced as a further primitive predicate and axiomatized. The semantics and proof theory of $\mathsf {CD}$ are analyzed. [ABSTRACT FROM AUTHOR]

We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using interactive and automated reasoning tools. This enables the formal analysis and verification of meta-theoretical properties as well as the flexible generation of extensions and labellings with respect to well-known argumentation semantics. [ABSTRACT FROM AUTHOR]

We focus on the persistence principle over weak interpretability logic. Our object of study is the logic obtained by adding the persistence principle to weak interpretability logic from several perspectives. Firstly, we prove that this logic enjoys a weak version of the fixed point property. Secondly, we introduce a system of sequent calculus and prove the cut‐elimination theorem for it. As a consequence, we prove that the logic enjoys the Craig interpolation property. Thirdly, we show that the logic is the natural basis of a generalization of simplified Veltman semantics, and prove that it has the finite frame property with respect to that semantics. Finally, we prove that it is sound and complete with respect to some appropriate arithmetical semantics. [ABSTRACT FROM AUTHOR]

The semantic analysis of conditional sentences does not entirely align with their morphosyntactic structure. I substantiate this hypothesis with instances from both Czech and English that extend beyond conventional textbook examples. I also highlight that logicians and philosophers often make terminological errors when they disregard the insights from linguistic disciplines. Despite the early analytic philosophy’s emphasis on terminological precision, the practical application falls significantly short of this ideal. I firmly believe that a proper understanding of the morphosyntax and semantics of conditional sentences is a prerequisite for their classification and analysis. In our pursuit of a comprehensive exploration of conditional clauses, we must also grapple with methodological challenges that delve into the very core of the philosophy of language. The primary issue revolves around the fact that two out of the three a priori methods in philosophy rely heavily on the analysis of conditional sentences: thought experiments and modal metaphysics. [ABSTRACT FROM AUTHOR]

Modal logic enjoys topological semantics that may be traced back to McKinsey and Tarski, and the classification of topological spaces via modal axioms is a lively area of research. In the past two decades, there has been interest in extending topological modal logic to the language of the mu-calculus, but previously no class of topological spaces was known to be mu-calculus definable that was not already modally definable. In this paper, we show that the full mu-calculus is indeed more expressive than standard modal logic, in the sense that there are classes of topological spaces (and weakly transitive Kripke frames), which are mu-definable but not modally definable. The classes we exhibit satisfy a modally definable property outside of their perfect core, and thus we dub them imperfect spaces. We show that the mu-calculus is sound and complete for these classes. Our examples are minimal in the sense that they use a single instance of a greatest fixed point, and we show that least fixed points alone do not suffice to define any class of spaces that is not already modally definable. [ABSTRACT FROM AUTHOR]

This paper explores the interplay between logic-sensitivity and bitstring semantics in the square of opposition. Bitstring semantics is a combinatorial technique for representing the formulas that appear in a logical diagram, while logic-sensitivity entails that such a diagram may depend, not only on the formulas involved, but also on the logic with respect to which they are interpreted. These two topics have already been studied extensively in logical geometry, and are thus well-understood by themselves. However, the precise details of their interplay turn out to be far more complicated. In particular, the paper describes an elegant and natural interaction between bitstrings and logic-sensitivity, which makes perfect sense when bitstrings are viewed as purely combinatorial entities. However, when we view bitstrings as semantically meaningful entities (which is actually the standard perspective, cf. the term 'bitstring semantics'!), this interaction does not seem to have a full and equally natural counterpart. The paper describes some attempts to address this situation, but all of them are ultimately found wanting. For now, it thus remains an open problem to capture this interaction between bitstrings and logic-sensitivity from a semantic (rather than merely a combinatorial) perspective. [ABSTRACT FROM AUTHOR]

In this paper we will consider the existing notions of bilateralism in the context of proof-theoretic semantics and propose, based on our understanding of bilateralism, an extension to logical multilateralism. This approach differs from what has been proposed under this name before in that we do not consider multiple speech acts as the core of such a theory but rather multiple consequence relations. We will argue that for this aim the most beneficial proof-theoretical realization is to use sequent calculi with multiple sequent arrows satisfying some specific conditions, which we will lay out in this paper. We will unfold our ideas with the help of a case study in logical tetralateralism and present an extension of Almukdad and Nelson's propositional constructive four-valued logic by unary operations of meaningfulness and nonsensicality. We will argue that in sequent calculi with multiple sequent arrows it is possible to maintain certain features that are desirable if we assume an understanding of the meaning of connectives in the spirit of proof-theoretic semantics. The use of multiple sequent arrows will be justified by the presence of congruentiality-breaking unary connectives. [ABSTRACT FROM AUTHOR]

The semantic analysis of conditional sentences does not entirely align with their morphosyntactic structure. I substantiate this hypothesis with instances from both Czech and English that extend beyond conventional textbook examples. I also highlight that logicians and philosophers often make terminological errors when they disregard the insights from linguistic disciplines. Despite the early analytic philosophy’s emphasis on terminological precision, the practical application falls significantly short of this ideal. I firmly believe that a proper understanding of the morphosyntax and semantics of conditional sentences is a prerequisite for their classification and analysis. In our pursuit of a comprehensive exploration of conditional clauses, we must also grapple with methodological challenges that delve into the very core of the philosophy of language. The primary issue revolves around the fact that two out of the three a priori methods in philosophy rely heavily on the analysis of conditional sentences: thought experiments and modal metaphysics.

Artificial intelligence (AI) has posed numerous legal--ethical challenges. These challenges are particularly acute when dealing with AI demonstrating substantial computational prowess, which is then correlated with agency or autonomy. A common response to considering this issue is to inquire whether an AI system is "conscious" or not. If it is, then it could constitute an agent, actor, or person. This framing is, however, unhelpful since there are many unresolved questions about consciousness. Instead, a practical approach is proposed, which could be used to better regulate new AI technologies. The value of the practical approach in this study is that it (1) provides an empirically observable, testable framework that contains predictive value; (2) is derived from a data-science framework that uses semantic information as amarker; (3) relies on a self-referential logic which is fundamental to agency; (4) enables the "grading" or "ranking" of AI systems, which provides an alternative method (as opposed to current risk-tiering approaches) and measure to determine the suitability of an AI system within a specific domain (e.g., such as social domains or emotional domains); (5) presents consistent, coherent, and higher informational content as opposed to other approaches; (6) fits within the conception of what informational content "laws" are to contain and maintain; and (7) presents a viable methodology to obtain "agency", "agent", and "personhood", which is robust to current and future developments in AI technologies and society. [ABSTRACT FROM AUTHOR]

Natural language does not express all connectives definable in classical logic as simple lexical items. Coordination in English is expressed by conjunction and, disjunction or, and negated disjunction nor. Other languages pattern similarly. Non-lexicalized connectives are typically expressed compositionally: in English, negated conjunction is typically expressed by combining negation and conjunction (not both). This is surprising: if ∧ and ∨ are duals, and the negation of the latter can be expressed lexically (nor), why not the negation of the former? I present a two-tiered model of the semantics of the binary connectives. The first tier captures the expressive power of the lexicon: it is a bilateral state-based semantics that, under a restriction, can express all and only the distinctions that can be expressed by the lexicon of natural language (and, or, nor). This first tier is characterized by rejection as non-assertion and a Neglect Zero assumption. The second tier is obtained by dropping the Neglect Zero assumption and enforcing a stronger notion of rejection, thereby recovering classical logic and thus definitions for all Boolean connectives. On the two-tiered model, we distinguish the limited expressive resources of the lexicon and the greater combinatorial expressive power of the language as a whole. This gives us a logic-based account of compositionality for the Boolean fragment of the language. [ABSTRACT FROM AUTHOR]

In Die Grundgesetze der Arithmetik (I, §48), Frege introduces his rule of the fusion of horizontals, according to which if an occurrence of the horizontal stroke is followed by another occurrence of the same stroke, either in isolation or "contained" in a propositional connective, the two occurrences can be fused with each other. However, the role of this rule, and of the horizontal sign more generally, is controversial; Michael Dummett notoriously claimed, for instance, that the horizontal is "wholly superfluous" in Frege's logical system. In this paper, we challenge Dummett's view by providing a comprehensive analysis of the significance of the horizontal stroke. After some preliminary remarks, we argue that even if Frege's connectives in some sense "contain" the horizontal, yet they are total functions. Then, we take up the question of the sense expressed by the horizontal, and we claim that, unlike other sentential operators, the horizontal is not sense‐compositional. Finally, we consider the semantic and pragmatic aspects of Frege's horizontal in connection to his judgment stroke and the double judgment stroke. Contra Dummett, we argue that the horizontal is a special and indispensable element of Frege's logic. [ABSTRACT FROM AUTHOR]

Causal models show promise as a foundation for the semantics of counterfactual sentences. However, current approaches face limitations compared to the alternative similarity theory: they only apply to a limited subset of counterfactuals and the connection to counterfactual logic is not straightforward. This article addresses these difficulties using exogenous interventions, where causal interventions change the values of exogenous variables rather than structural equations. This model accommodates judgments about backtracking counterfactuals, extends to logically complex counterfactuals, and validates familiar principles of counterfactual logic. This combines the interventionist intuitions of the causal approach with the logical advantages of the similarity approach. [ABSTRACT FROM AUTHOR]

This study focuses on a factor known to increase sentence processing complexity – negation. We sought to distill out of negation a logical property – Inference Reversal – to see whether it, and not an actual negation word, determines this complexity. First, we tested a negation-less pair of polar operators (at most, at least) in Hebrew. We found that processing time for sentences containing the Inference Reversing at most lagged behind those with at least. Second, we compared the processing of sentences containing two Inference Reversing operators (not less) to sentences with zero (ø, more) and one (not more, less). Since two Inference Reversing Operators annul Inference Reversal ("two negatives make a positive"), we asked whether their processing cost is annulled, or rather cumulative. Surprisingly, RTnot less was shorter than RTnot more. These findings lead to the conclusion that even when covert, Inference Reversal is an important determinant of processing complexity. [ABSTRACT FROM AUTHOR]

We present a critical analysis of Newton da Costa's C1 paraconsistent calculus. The strategy considers what we call semantic categories underlying a logic, from which we explore a broader notion of meaning for the logic than the one provided by formal semantics. Through the examination of the semantic categories associated in principle with this calculus, and the analysis of a rational reconstruction of a historical case of inconsistency, we argue that there is a certain inadequacy within the semantic structure of C1, understood in the more general framework of meaning; we also argue that there is an inadequacy between this general semantic structure and those semantic categories of scientific thought that it would be modeling. From all the above, we conclude a brief argument in favor of the idea that scientific contradictions should preferably be modeled (against, at least, some of the hegemonic proposals) as necessarily false formulae. [ABSTRACT FROM AUTHOR]

Is it possible to maintain classical logic, stay close to classical semantics, and yet accept that language might be semantically indeterminate? The article gives an affirmative answer by Ramsifying classical semantics , which yields a new semantic theory that remains much closer to classical semantics than supervaluationism but which at the same time avoids the problematic classical presupposition of semantic determinacy. The resulting Ramsey semantics is developed in detail, it is shown to supply a classical concept of truth and to fully support the rules and metarules of classical logic, and it is applied to vague terms as well as to theoretical or open-ended terms from mathematics and science. The theory also demonstrates how diachronic or synchronic interpretational continuity across languages is compatible with semantic indeterminacy. [ABSTRACT FROM AUTHOR]

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The development of sensor networks allows for easier time series data acquisition in industrial production. Due to the redundancy and rapidity of industrial time series data, accurate anomaly detection is a complex and important problem for the efficient production of the textile process. This paper proposed a semantic inference method for anomaly detection by constructing the formal specifications of anomaly data, which can effectively detect exceptions in process industrial operations. Furthermore, our method provides a semantic interpretation of exception data. Hybrid signal temporal logic (HSTL) was proposed to improve the insufficient expressive ability of signal temporal logic (STL) systems. The epistemic formal specifications of fault offline were determined, and a data-driven semantic anomaly detector (SeAD) was constructed, which can be used for online anomaly detection, helping people understand the causes and effects of anomalies. Our proposed method was applied to time-series data collected from a representative textile plant in Zhejiang Province, China. Comparative experimental results demonstrated the feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

In this note we define a new two-state logic, called 2neg-logic (logic with two negations) and compare its expressive power with other two-state logics, such as the logic of here-and-there, contingency logic, and bi-state logic. [ABSTRACT FROM AUTHOR]

Generalising the attack structure in argumentation frameworks (AFs) has been studied in different ways. Most prominently, the binary attack relation of Dung frameworks has been extended to the notion of collective attacks. The resulting formalism is often termed SETAFs. Among the generalisations of AFs, abstract dialectical frameworks (ADFs) allow for a systematic and flexible generalisation of AFs in which different kinds of logical relations, e.g. attack and support, among arguments can be represented. Restricting the logical relations among arguments leads to different subclasses of ADFs of interest. In this work, we consider so-called support-free ADFs that allow for all kinds of attacks but no support or other relations and SETADFs that embed SETAFs in the ADF setting. The aim of this paper is to shed light on the relation between these two different approaches. To this end, we investigate and compare the expressiveness of SETAFs and support-free ADFs under the lens of 3-valued semantics. Our results show that it is only the presence of unsatisfiable acceptance conditions in support-free ADFs that discriminates the two approaches. [ABSTRACT FROM AUTHOR]

Over the past decades, Patricia Blanchette has developed a sophisticated account of Frege's conception of logic and his views on logical consequence. One of the central components of her interpretation is the idea that Frege's conception of logical consequence is 'semantically laden' and not purely formal. The aim of the present paper is to provide precise explications of this as well as related ideas that inform her account, and to discuss their significance for the philosophy of logic in general and Frege's philosophy in particular. [ABSTRACT FROM AUTHOR]

According to Schroeder-Heister 2018, proof-theoretic semantics is 'an alternative to truth-condition semantics. It is based on the fundamental assumption that the central notion in terms of which meanings are assigned to certain expressions of our language, in particular to logical constants, is that of proof rather than truth. In this sense proof-theoretic semantics is semantics in terms of proof. Proof-theoretic semantics also means the semantics of proofs, i.e. the semantics of entities which describe how we arrive at certain assertions given certain assumptions.' This text advocates that proof-theoretic semantics, as described above, was an approach to semantical issues in logic that appeared in mainstream philosophical literature at least a couple of centuries before the tradition of general proof theory (cf. Prawitz 1971) came into being. This is done by means of an interpretive analysis of Kant's 1762 essay Die falsche Spitzfindigkeit der vier syllogistischen Figuren, in which two theses are argued: first, that the issue of justifying the logical validity of inferences is approached by Kant in this text, in a strong sense, in terms of proofs; and second, that the purpose of his effort is to establish a point concerning the semantical equivalence between certain distinct valid inferences. [ABSTRACT FROM AUTHOR]

In this essay I propose two theories of truth and show how they deal with semantic paradoxes. Their most salient feature is that they are based on a gametheoretic understanding of logic and meaning. "Truth", therefore, is understood dialogically, as agreement between parts. I compare this proposal with a similar one already existing in the literature --Dutilh Novaes and French 2018--, and highlight the advantages of mine. The theories of truth I present are non-trivial, substructural (in a sense to be clarified) and capture strong intuitions about truth. Some philosophical recommendations in favor of our understanding of Dialogics are delivered along the way. [ABSTRACT FROM AUTHOR]

Call a truth complete with respect to a subject matter if it entails every truth about that subject matter. One attractive way to formulate a complete truth is to state all the relevant positive truths, and then add: and that's it. When the subject matters under consideration are non-contingent, a non-trivial conception of completeness must invoke a hyperintensional conception of entailment, and of the completion operation denoted by 'that's it'. This paper develops two complementary hyperintensional conceptions of completion using the framework of truthmaker semantics and determines the resulting logics of totality. [ABSTRACT FROM AUTHOR]

Putting individual constants and quantifiers into the same syntactic category within first-order language promises to have far-reaching consequences: a syntax of this kind can reveal the potential of any such language, allowing us to realize that a vast class of noun phrases, including non-denoting terms, can be accommodated in the new syntax as expressions suited to being subjects of sentences. In the light of this, a formal system that is an extension of classical first-order logic is developed here, and is equipped with an appropriate semantics. An ontological interpretation of the new logic is then also provided, with several categories of object and notions of existence being distinguished. Last but not least, a modal version of the logic, with some interesting formal features, is proposed. [ABSTRACT FROM AUTHOR]

We give a novel approach to proving soundness and completeness for a logic (henceforth: the object-logic) that bypasses truth-in-a-model to work directly with validity. Instead of working with specific worlds in specific models, we reason with eigenworlds (i.e., generic representatives of worlds) in an arbitrary model. This reasoning is captured by a sequent calculus for a meta-logic (in this case, first-order classical logic) expressive enough to capture the semantics of the object-logic. Essentially, one has a calculus of validity for the object-logic. The method proceeds through the perspective of reductive logic (as opposed to the more traditional paradigm of deductive logic), using the space of reductions as a medium for showing the behavioural equivalence of reduction in the sequent calculus for the object-logic and in the validity calculus. Rather than study the technique in general, we illustrate it for the logic of Bunched Implications (BI), thus IPL and MILL (without negation) are also treated. Intuitively, BI is the free combination of intuitionistic propositional logic and multiplicative intuitionistic linear logic, which renders its meta-theory is quite complex. The literature on BI contains many similar, but ultimately different, algebraic structures and satisfaction relations that either capture only fragments of the logic (albeit large ones) or have complex clauses for certain connectives (e.g., Beth's clause for disjunction instead of Kripke's). It is this complexity that motivates us to use BI as a case-study for this approach to semantics. [ABSTRACT FROM AUTHOR]

Change of logic is typically taken as requiring that the meanings of the connectives change too. As a result, it has been argued that legitimate rivalry between logics is under threat. This is, in a nutshell, the meaning‐variance argument, traditionally attributed to Quine. In this paper, we present a semantic framework that allows us to resist the meaning‐variance claim for an important class of systems: classical logic, the logic of paradox and strong Kleene logic. The major feature of the semantics is that the connectives have the same meanings in these systems, so that the meaning‐variance argument is straightforwardly blocked. We discuss the effects of this semantics for two uses of the argument of meaning variance, and also consider its impact on related issues. [ABSTRACT FROM AUTHOR]

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We consider an approach to propositional synonymy in proof-theoretic semantics that is defined with respect to a bilateral G3-style sequent calculus SC2Int for the bi-intuitionistic logic 2Int. A distinctive feature of SC2Int is that it makes use of two kinds of sequents, one representing proofs, the other representing refutations. The structural rules of SC2Int, in particular its cut rules, are shown to be admissible. Next, interaction rules are defined that allow transitions from proofs to refutations, and vice versa, mediated through two different negation connectives, the well-known implies-falsity negation and the less well-known coimplies-truth negation of 2Int. By assuming that the interaction rules have no impact on the identity of derivations, the concept of inherited identity between derivations in SC2Int is introduced and the notions of positive and negative synonymy of formulas are defined. Several examples are given of distinct formulas that are either positively or negatively synonymous. It is conjectured that the two conditions cannot be satisfied simultaneously. [ABSTRACT FROM AUTHOR]

Questions concerning the proof-theoretic strength of classical versus nonclassical theories of truth have received some attention recently. A particularly convenient case study concerns classical and nonclassical axiomatizations of fixed-point semantics. It is known that nonclassical axiomatizations in four- or three-valued logics are substantially weaker than their classical counterparts. In this paper we consider the addition of a suitable conditional to First-Degree Entailment—a logic recently studied by Hannes Leitgeb under the label HYPE. We show in particular that, by formulating the theory PKF over HYPE , one obtains a theory that is sound with respect to fixed-point models, while being proof-theoretically on a par with its classical counterpart KF. Moreover, we establish that also its schematic extension—in the sense of Feferman—is as strong as the schematic extension of KF , thus matching the strength of predicative analysis. [ABSTRACT FROM AUTHOR]

Most ordinary objects - cats, humans, mountains, ships, tables, etc. - have indeterminate mereological boundaries. If the theory of mereology is meant to include ordinary objects at all, we need it to have some space for mereological indeterminacy. In this paper, we present a novel degree-theoretic semantics - Boolean semantics - and argue that it is the best degree-theoretic semantics for modeling mereological indeterminacy, for three main reasons: (a) it allows for incomparable degrees of parthood, (b) it enforces classical logic, and (c) it is compatible with all the axioms of classical mereology. Using Boolean semantics, we will also investigate the connection between vagueness in parthood and vagueness in existence/identity. We show that, contrary to what many have argued, the connection takes neither the form of entailment nor the form of exclusion. [ABSTRACT FROM AUTHOR]

We study arbitrary intermediate propositional logics extended with a collection of axioms from (classical) justification logics. For these, we introduce various semantics by combining either Heyting algebras or Kripke frames with the usual semantic machinery used by Mkrtychev's, Fitting's or Lehmann and Studer's models for classical justification logics. We prove unified completeness theorems for all intermediate justification logics and their corresponding semantics using a respective propositional completeness theorem of the underlying intermediate logic. Further, by a modification of a method of Fitting, we prove unified realization theorems for a large class of intermediate justification logics and accompanying intermediate modal logics. [ABSTRACT FROM AUTHOR]

In the present paper, we obtain a Jónsson-style canonicity proof for the Sahlqvist fragment of distributive modal |$\mu $| -calculus in clopen semantics, alternative to the canonicity-via-correspondence argument in Conradie and Craig (2017, Journal of Logic and Computation , 27, 705–748), generalizing the results in Bezhanishvili and Hodkinson (2012, Theoretical Computer Science , 424, 1–19). The key ingredient of this proof is a characterization result about |$\sigma $| -contracting maps. [ABSTRACT FROM AUTHOR]