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In English, a sentence like "The cat didn't eat the carrot or the pepper" typically receives a "neither" interpretation; in Japanese it receives a "not this or not that" interpretation. These two interpretations are in a subset/superset relation, such that the "neither" interpretation (strong reading) asymmetrically entails the "not this or not that" interpretation (weak reading). This asymmetrical entailment raises a learnability problem. According to the Semantic Subset Principle, all language learners, regardless of the language they are exposed to, start by assigning the strong reading, since this interpretation makes such sentences true in the narrowest range of circumstances.). If the "neither" interpretation is children's initial hypothesis, then children acquiring a superset language will be able to revise their initial hypothesis on the basis of positive evidence. The aim of the present study is to test an additional account proposed by Pagliarini, Crain, Guasti (2018) as a possible explanation for the earlier convergence to the adult grammar by Italian children. The hypothesis tested here is that the presence of a lexical form such as recursive né that unambiguously conveys a "neither" meaning, would lead children to converge earlier to the adult grammar due to a blocking effect of the recursive né form in the inventory of negated disjunction forms in a language. We compared data from Italian (taken from Pagliarini, Crain, Guasti, 2018), French, Hungarian and Dutch. Dutch was tested as baseline language. French and Hungarian have – similarly to Italian – a lexical form that unambiguously expresses the "neither" interpretation (ni ni and sem sem, respectively). Our results did not support this hypothesis however, and are discussed in the light of language-specific particularities of the syntax and semantics of negation. [ABSTRACT FROM AUTHOR]

Sentences about logic are often used to show that certain embedding expressions (attitude verbs, conditionals, etc.) are hyperintensional. Yet it is not clear how to regiment "logic talk" in the object language so that it can be compositionally embedded under such expressions. In this paper, I develop a formal system called hyperlogic that is designed to do just that. I provide a hyperintensional semantics for hyperlogic that doesn't appeal to logically impossible worlds, as traditionally understood, but instead uses a shiftable parameter that determines the interpretation of the logical connectives. I argue this semantics compares favorably to the more common impossible worlds semantics, which faces difficulties interpreting propositionally quantified logic talk. [ABSTRACT FROM AUTHOR]

In this paper we show that, when analyzed with contemporary tools in logic—such as Dunn-style semantics, Reichenbach's three-valued logic exhibits many interesting features, and even new responses to some of the old objections to it can be attempted. Also, we establish some connections between Reichenbach's three-valued logic and some contra-classical logics. [ABSTRACT FROM AUTHOR]

Non-bivalent semantics of the future tense assert that propositions regarding future contingents are neither true nor false. One of the most relevant non-bivalent semantics is supervaluationism (Thomason in Theoria 36(3):264–281, 1970; Thomason, in: Gabbay, Guenthner (eds) Handbook of philosophical logic, Springer, Berlin, 1984), which preserves important logical principles. Recently, non-bivalent semantics are under attack from some pragmatics arguments: these semantics would be incompatible with our practices of asserting future contingents and with the probability we ascribe to such assertions (Besson and Hattiangadi in Philosophical Studies 167(2):251–271, 2014; Cariani and Santorio in Mind 127(505):129–165, 2018). The aim of this paper is to defend supervaluationism against this kind of criticism. We argue that, if probability is interpreted as the subjective belief in a proposition and if a semantic contextualism is adopted, supervaluationism makes correct predictions concerning the norms that govern our practices of asserting future contingents. Obviously, other arguments can be proposed against supervaluationism, but they must be of a different kind, such as metaphysical arguments. [ABSTRACT FROM AUTHOR]

What does logic tells us how about we ought to reason? If P entails Q, and I believe P, should I believe Q? I will argue that we should embed the issue in an independently motivated contextualist semantics for 'ought', with parameters for a standard and set of propositions. With the contextualist machinery in hand, we can defend a strong principle expressing how agents ought to reason while accommodating conflicting intuitions. I then show how our judgments about blame and guidance can be handled by this machinery. [ABSTRACT FROM AUTHOR]

In this article, we present an approach based on counterexample-guided abstraction refinement to verifying full regular temporal properties of C programs by means of combining both static analysis and dynamic verification. To this end, a desired property is specified by a propositional projection temporal logic formula $p$ , and the labeled normal form graph (LNFG) of $\lnot p$ is automatically produced. Furthermore, the control flow automaton of the C program is constructed, and an enriched abstract reachability tree is generated under the guidance of the LNFG. Throughout the construction of the eART, whenever a candidate counterexample $cp$ is found, a verification input w.r.t $cp$ is generated by the SMT solver Z3. Subsequently, the C program is converted into a modeling, simulation, and verification language (MSVL) program $m$ , and $\lnot p$ is also transformed to an MSVL program $m^{\prime }$. As a result, $m\; \text{and} \;m^{\prime }$ is executed to check whether the counterexample is spurious. The $cp$ is returned if it is a real counterexample; otherwise, the eART is refined. This process is repeated until no counterexample is found, namely the property is valid, or the counterexample is a real one The proposed approach enables us to not only verify full regular properties of C programs, but also produce precise results, neither false negatives nor false positives. The approach has been implemented in a tool named SDMC. Experiments show that SDMC outperforms the relevant tools available. [ABSTRACT FROM AUTHOR]

This paper develops a theory of propositional identity which distinguishes necessarily equivalent propositions that differ in subject-matter. Rather than forming a Boolean lattice as in extensional and intensional semantic theories, the space of propositions forms a non-interlaced bilattice. After motivating a departure from tradition by way of a number of plausible principles for subject-matter, I will provide a Finean state semantics for a novel theory of propositions, presenting arguments against the convexity and nonvacuity constraints which Fine (Journal of Philosophical Logic, 4545, 199–226 13, 14, 15) introduces. I will then move to compare the resulting logic of propositional identity (PI1) with Correia's (The Review of Symbolic Logic, 9, 103–122 9) logic of generalised identity (GI), as well as the first degree fragment of Angell's (2) logic of analytic containment (AC). The paper concludes by extending PI1 to include axioms and rules for a subject-matter operator, providing a much broader theory of subject-matter than the principles with which I will begin. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 modeling 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. [ABSTRACT FROM AUTHOR]

In this paper we present the history of and the research directions in relating logic. For this purpose we will describe Epstein's Programme, which postulates accounting for the content of sentences in logical research. We will focus on analysing the content relationship and Epstein's logics that are based on it, which are special cases of relating logic. Moreover, the set-assignment semantics will be discussed. Next, the Torunian Programme of Relating Semantics will be presented; this programme explores the various non-logical relationships in logical research, including those which are content-related. We will present a general description of relating logic and semantics as well as the most prominent issues regarding the Torunian Programme, including some of its special cases and the results achieved to date. [ABSTRACT FROM AUTHOR]

Recently, in an ongoing debate about informal provability, non-deterministic logics of informal provability BAT and CABAT were developed to model the notion. CABAT logic is defined as an extension of BAT logics and itself does not have independent and decent semantics. The aim of the paper is to show that, semantically speaking, both logics are rather complex and they can be characterized by neither finitely many valued deterministic semantics nor possible word semantics including neighbourhood semantics. [ABSTRACT FROM AUTHOR]

Prawitz (1971) conjectured that proof-theoretic validity offers a semantics for intuitionistic logic. This conjecture has recently been proven false by Piecha and Schroeder-Heister (2019). This article resolves one of the questions left open by this recent result by showing the extensional alignment of proof-theoretic validity and general inquisitive logic. General inquisitive logic is a generalisation of inquisitive semantics, a uniform semantics for questions and assertions. The paper further defines a notion of quasi-proof-theoretic validity by restricting proof-theoretic validity to allow double negation elimination for atomic formulas and proves the extensional alignment of quasi-proof-theoretic validity and inquisitive logic. [ABSTRACT FROM AUTHOR]

In the literature on self-referential paradoxes one of the hardest and most challenging problems is that of revenge. This problem can take many shapes, but, typically, it besets non-classical accounts of some semantic notion, such as truth, that depend on a set of classically defined meta-theoretic concepts, like validity, consistency, and so on. A particularly troubling form of revenge that has received a lot of attention lately involves the concept of validity. The difficulty lies in that the non-classical logician cannot accept her own definition of validity because it is given in a classical meta-theory. It is often suggested that this mismatch between the consequence relation of the account being espoused and the consequence relation of the meta-theory is a serious embarrassment. The main goal of the paper is to explore whether certain substructural accounts of the paradoxes can avoid this sort of embarrassment. Typically, these accounts are expressively incomplete, since they cannot assert in the object language that certain invalid arguments are in fact invalid. To overcome this difficulty I develop a novel type of hybrid proof-procedure, one that takes invalidities to be just as fundamental as validities. I prove that this proof-procedure enjoys a number of interesting properties and I analyze the prospects of applying it to languages capable of expressing self-referential statements. [ABSTRACT FROM AUTHOR]

In this paper, I will defend a new compositional semantics for single-domain free logic. This semantics makes use of a distinction between the semantic value of a singular term and its semantic referent. The semantic value of a singular term is conceived of as a set that either contains the semantic referent or no element at all. The semantic referent is the object that the term designates. Before I will introduce this new semantics for single-domain predicate and an S5-type modal logic in detail, I will present five related problems of compositionality of the standard semantics for these logical systems. After that I will show in detail how my new proposed alternative semantics can be used to solve nearly all of the outlined five problems. [ABSTRACT FROM AUTHOR]

Let V be a set of number-theoretical functions. We define a notion of absolute V -realizability for predicate formulas and sequents in such a way that the indices of functions inV are used for interpreting the implication and the universal quantifier. In this article, we prove that Basic Predicate Calculus is sound with respect to the semantics of absolute V -realizability if V satisfies some natural conditions. [ABSTRACT FROM AUTHOR]

Two-dimensional semantics, which can represent the distinction between a priority and (one kind of) necessity, has wielded considerable influence in the philosophy of language. In this paper, I axiomatize the dagger († ) operator of Stalnaker's "Assertion" (1978) in the formal context of two-dimensional modal logic. The language contains modalities of actuality, necessity, and a priority, but is also able to represent diagonalization, a conceptually important operation in a variety of contexts, including models of the relative a priori and a posteriori often appealed to Bayesian and Gricean contexts. Finally, I sketch the prospects for extending this two-dimensional upgrade to other kinds of modal logics for natural language. [ABSTRACT FROM AUTHOR]

Logic programs with ordered disjunction (LPODs) extend classical logic programs with the capability of expressing alternatives with decreasing degrees of preference in the heads of program rules. Despite the fact that the operational meaning of ordered disjunction is clear, there exists an important open issue regarding its semantics. In particular, there does not exist a purely model-theoretic approach for determining the most preferred models of an LPOD. At present, the selection of the most preferred models is performed using a technique that is not based exclusively on the models of the program and in certain cases produces counterintuitive results. We provide a novel, model-theoretic semantics for LPODs, which uses an additional truth value in order to identify the most preferred models of a program. We demonstrate that the proposed approach overcomes the shortcomings of the traditional semantics of LPODs. Moreover, the new approach can be used to define the semantics of a natural class of logic programs that can have both ordered and classical disjunctions in the heads of clauses. This allows programs that can express not only strict levels of preferences but also alternatives that are equally preferred. [ABSTRACT FROM AUTHOR]

Basic Logic BL, introduced by P. Hájek in 1998, is the logic of all continuous t-norms and their residua. The variety of BL-algebras forms the algebraic semantics of BL. Let L be a variety of BL-algebras, and let L (L) be its lattice of subvarieties, ordered by inclusion. L is called strictly join irreducible (SJI) if, whenever L is the join of a set S of varieties of BL-algebras, then L ∈ S. Every variety in L (L) is obtained as join of SJI varieties, which may be considered as the building blocks of all the varieties in L (L). In a previous work by the second author, a partial classification for the SJI varieties of BL-algebras has been found. In this paper we provide a full classification of the SJI varieties of BL-algebras. Our main result is that a variety of BL-algebras is SJI iff it is generated by a BL-chain with finitely many components, each of them being a cancellative hoop or a Wajsberg hoop with finite rank. As an application, we provide a characterization for the varieties of BL-algebras having only finitely many subvarieties, and we study some additional topics. [ABSTRACT FROM AUTHOR]

In the area of Natural Computing, Reaction Systems (RSs) are a qualitative abstraction inspired by the functioning of living cells, suitable to model the main mechanisms of biochemical reactions. RSs interact with a context, and pose challenges for modularity, compositionality, extendibility and behavioural equivalence. In this paper we define a modular encoding of RSs as processes in the chained Core Network Algebra (cCNA), which is a new variant of the link-calculus. The encoding represents the behaviour of each entity separately and preserves faithfully their features, and we prove its correctness and completeness. Our encoding provides a Labelled Transition System (LTS) semantics for RSs. Based on the LTS semantics, we adapt the classical notion of bisimulation to define a novel equivalence, called bio-similarity, for studying properties of RSs. In particular, we define a new assertion language based on regular expressions, which allows us to specify the properties of interest, and use it to extend Hennessy-Milner logic to our setting. We prove that our bio-similarity relation and the logical equivalence, that are defined parametrically on some assertion of interest, coincide. Finally, we claim that our encoding contributes to increase the expressiveness of RSs, by exploiting the interaction among different RSs. [ABSTRACT FROM AUTHOR]

We introduce so-called consistent posets which are bounded posets with an antitone involution ′ where the lower cones of x , x ′ and of y , y ′ coincide provided that x, y are different from 0, 1 and, moreover, if x, y are different from 0, then their lower cone is different from 0, too. We show that these posets can be represented by means of commutative meet-directoids with an antitone involution satisfying certain identities and implications. In the case of a finite distributive or strongly modular consistent poset, this poset can be converted into a residuated structure and hence it can serve as an algebraic semantics of a certain non-classical logic with unsharp conjunction and implication. Finally we show that the Dedekind–MacNeille completion of a consistent poset is a consistent lattice, i.e., a bounded lattice with an antitone involution satisfying the above-mentioned properties. [ABSTRACT FROM AUTHOR]

The similarity between logic and semantics of the Stoics and Frege has long been known, and it can be explained in various ways. In 2021, Susane Bobzien published a work in which she explains this similarity rather surprisingly: she hypothesizes that Frege generously helped himself with the foundations of Stoic logic as it was published in the first volume of History of Logic in the West by Carl Prantl. However, this hypothesis encounters various problems. The key point of the whole accusation is founded on the formulation of a general proposition in language using implication and anaphora, which Frege supposedly took from the Stoics, although in Prantl's text there is only one example of a sentence with this structure. On the contrary, there are many examples of such sentences in contemporary professional (e.g. legal) texts. Many examples of semantic similarities that Bobzien presents are based only on the similarities between isolated concepts; however, that is regularly the case for such concepts with the same conceptual basis. Bobzien presents a significant number of matches only on the basis of results that could allegedly be inferred from the texts. However, this cannot be considered a proof of plagiarism. Bobzien does not consider many sources for the continuity of interpretation such as the so-called hypothetical syllogism found in available textbooks of logic. Last but not least, her claims do not consider many differences between Stoic and Frege's logic. All this leads us to the conclusion that Bobzien does not present sufficient facts and connections between them that would confirm her hypothesis about Frege's plagiarism of the Stoic logic: Frege simply was not a plagiarist. [ABSTRACT FROM AUTHOR]

In Franceschi (2002), I presented a theory based on the matrices of concepts aiming at providing an alternative to the classification proposed by Greimas, in the field of paradigmatic analysis. The problem of specifying the relationships of the concepts of love, hate and indifference, arises in this construction. I attach myself to describe the problem of the love-hate-indifference relationships in detail, and several solutions that have been proposed to solve it. Finally I expose a solution to this problem, based on an extension of the theory of matrices of concepts.

Together with J. Paseka we introduced so-called sectionally pseudocomplemented lattices and posets and illuminated their role in algebraic constructions. We believe that—similar to relatively pseudocomplemented lattices—these structures can serve as an algebraic semantics of certain intuitionistic logics. The aim of the present paper is to define congruences and filters in these structures, derive mutual relationships between them and describe basic properties of congruences in strongly sectionally pseudocomplemented posets. For the description of filters in both sectionally pseudocomplemented lattices and posets, we use the tools introduced by A. Ursini, i.e., ideal terms and the closedness with respect to them. It seems to be of some interest that a similar machinery can be applied also for strongly sectionally pseudocomplemented posets in spite of the fact that the corresponding ideal terms are not everywhere defined. [ABSTRACT FROM AUTHOR]

Two interdependent phenomena are questioned: what allows, ecologically, the subject-environment relation then, the dynamics of this relation. To do this, two scientific currents are mobilized: affordance in its current meaning and the sociology of translation. While each of these currents has its own semantics and epistemology, both initiate breaks in the way of understanding what occurs within human activity and contribute to an ecological approach based on a fundamental principle: all human activity is situated and dynamic, characterizing the processes implemented by the actors according to the properties, in part, perceived of their socio-cultural environment. All deterministic logic is then set aside to place, on the same plane, all the dynamic entities within an environment, whether or not they are perceived by the actors on the ground. [ABSTRACT FROM AUTHOR]

This article deals with improved formal verification of reconfigurable discrete-event systems (DESs) modeled by reconfigurable timed net condition event systems (R-TNCESs). An R-TNCES consists of a set of timed net condition event systems, each of which represents a particular behavior of a DES, and a reconfiguration scenario is a switching mode from a timed net condition event system to another. However, the verification with the classical computation tree logic (CTL) as well as the related extensions increases the number of properties for complete verification of a complex R-TNCES. We propose reconfigurable CTL as a new extension of CTL to reduce such a number. New connectors of reconfigurable CTL are proposed, with their formal syntax and semantics, and a set of new algorithms is proposed to control the complexity of model checking. We use a benchmark production system for the performance evaluation of the proposed approach. Reduction in the number of properties to be checked is shown, and consequently, the related validation time is reduced. Note to Practitioners—This research represents a new orientation for guiding efficiently the model checking of reconfigurable discrete-event systems. A classification of properties described in computation tree logic (CTL), according to their dominance and equivalence relations, allows one to conduct an efficient verification by avoiding inefficient calculation due to redundant properties. In this case, giving a verification order for these properties allows one to shorten their verification time. An extension named reconfigurable CTL describes the new syntax of the proposed classification. This approach can be applied in modeling and verification of advanced reconfigurable systems arising from smart grids, adaptive sensor networks, intelligent transportation, reconfigurable manufacturing, and embedded systems. [ABSTRACT FROM AUTHOR]

Based on the Kripke structure, linear temporal logic and generalized possibility measure, this article studies the model checking problems of generalized possibilistic fuzzy linear temporal logic (GPoFTL). The generalized possibilistic Kripke structure is introduced to describe the system model. The syntax of GPoFTL, which includes fuzzy temporal operators such as ''soon'', ''presently'', ''gradually'', ''within'', ''last'', ''nearly always'', ''almost alwayss'', ''in the long distant future'', ''in the middle of'', ''nearly until'' and ''almost until'', and its language semantics and path semantics under generalized possibility measure are given. Next, we explain the semantics of fuzzy temporal operators through some examples and prove that GPoFTL is an extension of generalized possibilistic linear temporal logic in fuzzy time temporal logic. Furthermore, the GPoFTL model checking algorithm is given by explicit calculation formulas one by one for any GPoFTL formula involving fuzzy temporal operators using fuzzy matrix operations. Last, the algorithm of necessary threshold model checking of GPoFTL is studied using automata theory and its time complexity is discussed. [ABSTRACT FROM AUTHOR]

After putting forward a formal account of value disagreement via imprecise measures, I develop a logic of value attribution and of (dis)agreement based on (exact) truthmaker semantics. [ABSTRACT FROM AUTHOR]

A globally expressivist analysis of the indicative conditional based on the Ramsey Test is presented. The analysis is a form of 'global' expressivism in that it supplies acceptance and rejection conditions for all the sentence forming connectives of propositional logic (negation, disjunction, etc.) and so allows the conditional to embed in arbitrarily complex sentences (thus avoiding the Frege–Geach problem). The expressivist framework is semantically characterized in a restrictor semantics due to Vann McGee, and is completely axiomatized in a logic dubbed ICL ('Indicative Conditional Logic'). The expressivist framework extends the AGM (after Alchourron, Gärdenfors, Makinson) framework for belief revision and so provides a categorical ('yes'–'no') epistemology for conditionals that complements McGee's probabilistic framework while drawing on the same semantics. The result is an account of the semantics and acceptability conditions of the indicative conditional that fits well with the linguistic data (as pooled by linguists and from psychological experiments) while integrating both expressivist and semanticist perspectives. [ABSTRACT FROM AUTHOR]

In linguistics, the dominant approach to the semantics of plurals appeals to mereology. However, this approach has received strong criticisms from philosophical logicians who subscribe to an alternative framework based on plural logic. In the first part of the article, we offer a precise characterization of the mereological approach and the semantic background in which the debate can be meaningfully reconstructed. In the second part, we deal with the criticisms and assess their logical, linguistic, and philosophical significance. We identify four main objections and show how each can be addressed. Finally, we compare the strengths and shortcomings of the mereological approach and plural logic. Our conclusion is that the former remains a viable and well-motivated framework for the analysis of plurals. [ABSTRACT FROM AUTHOR]

This paper gives a semantics for schematic logic, proving soundness and completeness. The argument for soundness is carried out in ontologically innocent fashion, relying only on the existence of formulae which are actually written down in the course of a derivation in the logic. This makes the logic available to a nominalist, even a nominalist who does not wish to rely on modal notions, and who accepts the possibility that the universe may in fact be finite. [ABSTRACT FROM AUTHOR]

We propose in this paper a family of algebraic models of ZFC based on the three-valued paraconsistent logic LPT0, a linguistic variant of da Costa and D'Ottaviano's logic J3. The semantics is given by twist structures defined over complete Boolean agebras. The Boolean-valued models of ZFC are adapted to twist-valued models of an expansion of ZFC by adding a paraconsistent negation. This allows for inconsistent sets w satisfying 'not (w = w)', where 'not' stands for the paraconsistent negation. Finally, our framework is adapted to provide a class of twist-valued models generalizing Löwe and Tarafder's model based on logic (PS3,∗), showing that they are paraconsistent models of ZFC. The present approach offers more options for investigating independence results in paraconsistent set theory. [ABSTRACT FROM AUTHOR]

Let MK3 I and MK3 I I be Kleene's strong 3-valued matrix with only one and two designated values, respectively. Next, let MK3 G (resp., MK3 d G ) be defined exactly as MK3 I (resp., MK3 I I ), except that the characteristic Łukasiewicz-type negation of Kleene's strong 3-valued matrix is replaced by a 'Gödel-type' negation (resp., 'dual Gödel-type' negation). The aim of this paper is to axiomatize the logics determined by all natural implicative expansions of MK3 G and MK3 d G . The axiomatic formulations are defined by using a 'two-valued' Belnap-Dunn semantics. [ABSTRACT FROM AUTHOR]

Pretabularity is the attribute of logics that are not characterised by finite matrices, but all of whose proper extensions are. Two of the first-known pretabular logics were Dummett's famous super-intuitionistic logic LC and the well-known semi-relevance logic RM (= R-Mingle). In this paper, we investigate Anderson and Belnap's relevance logic R with the extra axiom: (p → q) ∨ (q → p), which we name LR, and which is (much) weaker than RM, and so is not pretabular. This means that over LR, there may be some pretabular extensions other than RM, two of which this paper presents and with which it provides axiomatizations, characteristic algebras, and Routley-Meyer semantics. [ABSTRACT FROM AUTHOR]

This note presents some new results from [1] about the Suszko operator and truth‐equational logics, following the works of Czelakowski [11] and Raftery [17]. It is proved that the Suszko operator relative to a truth‐equational logic S preserves suprema and commutes with endomorphisms. Together with injectivity, proved by Raftery in [17], the Suszko operator relative to a truth‐equational logic is a structural representation, as defined in [15]. Furthermore, if Alg(S) is a quasivariety, then the Suszko operator relative to a truth‐equational logic is continuous. Finally, it is proved that truth is equationally definable in the class LModSu(S) if and only if Alg(S) is a τ∞‐algebraic semantics for S and the Suszko operator Ω∼SFm:ThS→CoAlg(S)Fm preserves suprema and commutes with substitutions. [ABSTRACT FROM AUTHOR]

From the 1960s to the present day, Aristotelian aporias have been at the forefront of the question of the epistemological nature of first science. Authors vary from a purely dialectical interpretation of the aporias to an acquisitive interpretation of knowledge. The present article attempts to show the existence of objective, i.e. acquisitive aporias of knowledge. These aporias are based on an Aristotelian theory of objectivity which, overcoming the Platonic theory of contrariety, is expressed in his theory of contradiction, which bases the relation between reality and knowledge on the different levels of the metaphysical and logical structure of reality: semantic, propositional and inferential. Thus, objective aporias are those that express the determination of the object as substance and, from it, a possibility of reconciling the diaporematic method with Aristotelian epistemological realism. [ABSTRACT FROM AUTHOR]

Refinement relations, such as trace containment, simulation preorder, and their alternating versions, have been successfully applied in formal verification of concurrent systems. Recently, trace containment and simulation preorder have been adopted and developed in fuzzy systems, but the generalization of their alternating versions to fuzzy systems has not been investigated. To satisfy the need for modeling and analyzing fuzzy systems, this article proposes two types of refinement relations called fuzzy alternating trace containment and fuzzy alternating simulation preorder, based on fuzzy concurrent game structures (FCGSs) under the Gödel semantics. These two fuzzy notions inherit properties from the corresponding classical setting. For example, fuzzy alternating simulation preorder for finite-state FCGSs can be computed in polynomial time; fuzzy alternating simulation preorder is a fuzzy subset of fuzzy alternating trace containment, and both relations can be logically characterized in terms of fuzzy version of alternating-time temporal logic. These properties make the theory developed here suitable for the modeling and verification of fuzzy systems. [ABSTRACT FROM AUTHOR]

Three-valued logics are standardly used to formalize gappy languages, i.e., interpreted languages in which sentences can be true, false or neither. A three-valued logic that assigns the same truth value to all gappy sentences is, in our view, insufficient to capture important semantic differences between them. In this paper we will argue that there are two different kinds of pathologies that should be treated separately and we defend the usefulness of a four-valued logic to represent adequately these two types of gappy sentences. Our purpose is to begin the formal exploration of the four-valued logics that could be used to represent the phenomena in question and to show that these phenomena are present in natural language, at least according to some semantic theories of natural language. [ABSTRACT FROM AUTHOR]

In Part I of this paper, we identified and compared various schemes for trivalent truth conditions for indicative conditionals, most notably the proposals by de Finetti (1936) and Reichenbach (1935, 1944) on the one hand, and by Cooper (Inquiry, 11, 295–320, 1968) and Cantwell (Notre Dame Journal of Formal Logic, 49, 245–260, 2008) on the other. Here we provide the proof theory for the resulting logics DF/TT and CC/TT, using tableau calculi and sequent calculi, and proving soundness and completeness results. Then we turn to the algebraic semantics, where both logics have substantive limitations: DF/TT allows for algebraic completeness, but not for the construction of a canonical model, while CC/TT fails the construction of a Lindenbaum-Tarski algebra. With these results in mind, we draw up the balance and sketch future research projects. [ABSTRACT FROM AUTHOR]

This paper explores trivalent truth conditions for indicative conditionals, examining the "defective" truth table proposed by de Finetti (1936) and Reichenbach (1935, 1944). On their approach, a conditional takes the value of its consequent whenever its antecedent is true, and the value Indeterminate otherwise. Here we deal with the problem of selecting an adequate notion of validity for this conditional. We show that all standard validity schemes based on de Finetti's table come with some problems, and highlight two ways out of the predicament: one pairs de Finetti's conditional (DF) with validity as the preservation of non-false values (TT-validity), but at the expense of Modus Ponens; the other modifies de Finetti's table to restore Modus Ponens. In Part I of this paper, we present both alternatives, with specific attention to a variant of de Finetti's table (CC) proposed by Cooper (Inquiry 11, 295–320, 1968) and Cantwell (Notre Dame Journal of Formal Logic 49, 245–260, 2008). In Part II, we give an in-depth treatment of the proof theory of the resulting logics, DF/TT and CC/TT: both are connexive logics, but with significantly different algebraic properties. [ABSTRACT FROM AUTHOR]

The preferential conditional logic |$ \mathbb{PCL} $|⁠ , introduced by Burgess, and its extensions are studied. First, a natural semantics based on neighbourhood models, which generalizes Lewis' sphere models for counterfactual logics, is proposed. Soundness and completeness of |$ \mathbb{PCL} $| and its extensions with respect to this class of models are proved directly. Labelled sequent calculi for all logics of the family are then introduced. The calculi are modular and have standard proof-theoretical properties, the most important of which is admissibility of cut that entails a syntactic proof of completeness of the calculi. By adopting a general strategy, root-first proof search terminates, thereby providing a decision procedure for |$ \mathbb{PCL} $| and its extensions. Finally, semantic completeness of the calculi is established: from a finite branch in a failed proof attempt it is possible to extract a finite countermodel of the root sequent. The latter result gives a constructive proof of the finite model property of all the logics considered. [ABSTRACT FROM AUTHOR]

I introduce a proof system for the logic of relative fundamentality, as well as a natural semantics with respect to which the system is both sound and complete. I then "modalise" the logic, and finally I discuss the properties of grounding given a suggested account of this notion in terms of necessity and relative fundamentality. [ABSTRACT FROM AUTHOR]

We determine the modal logic of fixed-point models of truth and their axiomatizations by Solomon Feferman via Solovay-style completeness results. Given a fixed-point model $\mathcal {M}$ , or an axiomatization S thereof, we find a modal logic M such that a modal sentence $\varphi $ is a theorem of M if and only if the sentence $\varphi ^*$ obtained by translating the modal operator with the truth predicate is true in $\mathcal {M}$ or a theorem of S under all such translations. To this end, we introduce a novel version of possible worlds semantics featuring both classical and nonclassical worlds and establish the completeness of a family of noncongruent modal logics whose internal logic is nonclassical with respect to this semantics. [ABSTRACT FROM AUTHOR]

We characterize Weihrauch reducibility in $ \operatorname {\mathrm {E-PA^{\omega }}} + \operatorname {\mathrm {QF-AC^{0,0}}}$ and all systems containing it by the provability in a linear variant of the same calculus using modifications of Gödel's Dialectica interpretation that incorporate ideas from linear logic, nonstandard arithmetic, higher-order computability, and phase semantics. [ABSTRACT FROM AUTHOR]

Artificial intelligence (AI) research enjoyed an initial period of enthusiasm in the 1970s and 80s, but this enthusiasm was tempered by a long interlude of frustration when genuinely useful AI applications failed to be forthcoming. Today, we are experiencing once again a period of enthusiasm, fired above all by the successes of the technology of deep neural networks or deep machine learning. In this paper we draw attention to what we take to be serious problems underlying current views of artificial intelligence encouraged by these successes, especially in the domain of language processing. We then show an alternative approach to language-centric AI, in which we identify a role for philosophy. [ABSTRACT FROM AUTHOR]

A logical framework is presented to model legal interpretation and bring an appropriate construction of legal arguments. Reasoning with assumptions allows the construction of hypotheses. This is proposed in the context of legal procedures' dynamics, where the framework evolves as part of the investigation prior to each trial instance. Two gender-biased legal cases from the Argentinian jurisprudence are analyzed in the light of the proposed theory. Afterward, some proof standards for civil law systems are discussed as a way to define a specialized dialectical argumentation semantics. We claim that the application of the proposed theory would bring software assistance for controlling the influence of external factors of the law in the investigation of a legal case. [ABSTRACT FROM AUTHOR]

The present paper develops a unified correspondence treatment of the Sahlqvist theory for possibility semantics, extending the results in the work by Yamamoto (2016, Journal of Logic and Computation , 27 , 2411–2430) from Sahlqvist formulas to the strictly larger class of inductive formulas and from the full possibility frames to filter-descriptive possibility frames. Specifically, we define the possibility semantics version of the algorithm Ackermann lemma based algorithm (ALBA) and an adapted interpretation of the expanded modal language used in the algorithm. One notable feature of the adaptation of ALBA to possibility frames setting is that the so-called nominal variables, which are interpreted as complete join-irreducibles in the standard setting, are interpreted as regular open closures of 'singletons' in the present setting, which is a novelty of the present paper. We prove the soundness of the algorithm with respect to both (the dual algebras of) full possibility frames and (the dual algebras of) filter-descriptive possibility frames, use the algorithm to give an alternative proof to the one in the work by Holliday (2016, Possibility frames and forcing for modal logic. UC Berkeley Working Paper in Logic and the Methodology of Science. URL. http://escholarship.org/uc/item/9v11r0dq) that the inductive formulas are constructively canonical and show that the algorithm succeeds on inductive formulas. We make some comparisons among different semantic settings in the design of the algorithms and fit possibility semantics into this broader picture. [ABSTRACT FROM AUTHOR]

This paper provides some model-theoretic analysis for probability (modal) logic (⁠|$PL$|⁠). It is known that this logic does not enjoy the compactness property. However, by passing into the sublogic of |$PL$|⁠ , namely basic probability logic (⁠|$BPL$|⁠), it is shown that this logic satisfies the compactness property. Furthermore, by drawing some special attention to some essential model-theoretic properties of |$PL$|⁠ , a version of Lindström characterization theorem is investigated. In fact, it is verified that probability logic has the maximal expressive power among those abstract logics extending |$PL$| and satisfying both the filtration and disjoint unions properties. Finally, by alternating the semantics to the finitely additive probability models (⁠|$\mathcal{F}\mathcal{P}\mathcal{M}$|⁠) and introducing positive sublogic of |$PL$| including |$BPL$|⁠ , it is proved that this sublogic possesses the compactness property with respect to |$\mathcal{F}\mathcal{P}\mathcal{M}$|⁠. [ABSTRACT FROM AUTHOR]