Semantics Of Logic Research Articles

A basic system of paraconsistent Nelsonian logic of conditionals.

We define a Kripke semantics for a conditional logic based on the propositional logic , the paraconsistent variant of Nelson's logic of strong negation; we axiomatize the minimal system induced by this semantics. The resulting logic, which we call , shows strong connections both with the basic intuitionistic logic of conditionals introduced earlier in (Olkhovikov, 2023) and with the -based modal logic introduced in (Odintsov and Wansing, 2004) as one of the possible counterparts to the classical modal system . We map these connections by looking into the embeddings which obtain between the aforementioned systems.

A Propositional Cirquent Calculus for Computability Logic

Cirquent calculus is a proof system with inherent ability to account for sharing subcomponents in logical expressions. Within its framework, this article constructs an axiomatization CL18 of the basic propositional fragment of computability logic—the game-semantically conceived logic of computational resources and tasks. The nonlogical atoms of this fragment represent arbitrary so called static games, and the connectives of its logical vocabulary are negation and the parallel and choice versions of conjunction and disjunction. The main technical result of the article is a proof of the soundness and completeness of CL18 with respect to the semantics of computability logic.

Twardowskian Semantics for Performative Utterances

Works of Twardowski in the early 20th century contain an outline of a general semantic framework for natural languages. This framework, proposed within Twardowski’s theory of actions and ‘products,’ provides a drastic alternative to Frege’s semantic framework based on the notion of proposition (Gedanke in Frege). The latter has to a great extent shaped the following development of logical semantics. However, some recent works state that Twardowski’s theory allows to dissolve a number of problems characteristic of proposition-based semantics. In this paper, I show that it also provides a ground for a certain reconsideration of speech act theory. Since speech act theory was suggested by Austin as a fundamental alternative to standard proposition-oriented view on language, its emergence in a sense has divided philosophy of language into barely connected realms. The turn to Twardowskian semantics arguably allows to develop a more consistent understanding of how language works.

Semantics for Linear-time Temporal Logic with Finite Observations

Semantics for Linear-time Temporal Logic with Finite Observations

Truthmaker Semantics and Natural Language Semantics

ABSTRACTTruthmaker semantics is a non‐classical logical framework that has recently garnered significant interest in philosophy, logic, and natural language semantics. It redefines the propositional connectives and gives rise to more fine‐grained entailment relations than classical logic. In its model theory, truth is not determined with respect to possible worlds, but with respect to truthmakers, such as states or events. Unlike possible worlds, these truthmakers may be partial; they may be either coherent or incoherent; and they are understood to be exactly or wholly relevant to the truth of the sentences they verify. Truthmaker semantics generalises collective, fusion‐based theories of conjunction; alternative‐based theories of disjunction; and nonstandard negation semantics. This article provides a gentle introduction to truthmaker semantics aimed at linguists; describes applications to various natural language phenomena such as imperatives, ignorance implicatures, and negative events; and discusses its similarities and differences to related frameworks such as event semantics, situation semantics, alternative semantics, and inquisitive semantics.

The Rise of Logical Semantics in the Lvov‑Warsaw School: Introduction

The Rise of Logical Semantics in the Lvov‑Warsaw School: Introduction

Realization of logical meaning in Christian and Moslem Debate on Soco Films

This study is a critical discourse analysis study of metafunctions as part of the ideational function. And this research focus on the interpendency taxis system, namely parataxis and hypotaxis and relationship from logical semantics to expansion and projection in the analysis of Christian and Moslem Debate on SOCO films. By looking at the main focus and the overall analysis of this research, then study answered the following questions; what types of taxis are used in Christian and Moslem Debate on SOCO films and how the type of taxis are used in Christian and Moslem Debate on SOCO films. The Data were analized by descriptive qualitative analysis. The hypotaxis construction is more frequently occured than parataxis construction. It appears 136 times or 63.55%, meanwhile parataxis construction only appears 78 times or 36.45%.

Propositional logic and modal logic—A connection via relational semantics

Abstract In this paper, by slightly generalizing an observation of Dalla Chiara and Giuntini in their chapter on quantum logic in Handbook of Philosophical Logic, we propose a relational semantics for propositional language with negation and conjunction, which unifies the relational semantics of intuitionistic logic and that of ortho-logic. We study the semantic and syntactic consequence relations and prove the soundness and completeness theorems for five propositional logics: $\textbf{BL}$, $\textbf{PL}$, $\textbf{IL}$, $\textbf{OL}$ and $\textbf{CL}$. Moreover, we prove that they can be translated into the modal logics $\textbf{K}$, $\textbf{T}$, $\textbf{S4}$, $\textbf{KTB}$ and $\textbf{S5}$, respectively, and thus establish a systematic connection between propositional logics and modal logics. The paper ends with a discussion about the possibility and difficulty of incorporating disjunction into our framework.

A Rewriting-logic-with-SMT-based Formal Analysis and Parameter Synthesis Framework for Parametric Time Petri Nets

This paper presents a concrete and a symbolic rewriting logic semantics for parametric time Petri nets with inhibitor arcs (PITPNs), a flexible model of timed systems where parameters are allowed in firing bounds. We prove that our semantics is bisimilar to the “standard” semantics of PITPNs. This allows us to use the rewriting logic tool Maude, combined with SMT solving, to provide sound and complete formal analyses for PITPNs. We develop and implement a new general folding approach for symbolic reachability, so that Maude-with-SMT reachability analysis terminates whenever the parametric state-class graph of the PITPN is finite. Our work opens up the possibility of using the many formal analysis capabilities of Maude—including full LTL model checking, analysis with user-defined execution strategies, and even statistical model checking—for such nets. We illustrate this by explaining how almost all formal analysis and parameter synthesis methods supported by the state-of-the-art PITPN tool Roméo can be performed using Maude with SMT. In addition, we also support analysis and parameter synthesis from parametric initial markings, as well as full LTL model checking and analysis with user-defined execution strategies. Experiments show that our methods outperform Roméo in many cases.

Prawitz's completeness conjecture: A reassessment

AbstractIn 1973, Dag Prawitz conjectured that the calculus of intuitionistic logic is complete with respect to his notion of validity of arguments. On the background of the recent disproof of this conjecture by Piecha, de Campos Sanz and Schroeder‐Heister, we discuss possible strategies of saving Prawitz's intentions. We argue that Prawitz's original semantics, which is based on the principal frame of all atomic systems, should be replaced with a general semantics, which also takes into account restricted frames of atomic systems. We discard the option of not considering extensions of atomic systems, but acknowledge the need to incorporate definitional atomic bases in the semantic framework. It turns out that ideas and results by Westerståhl on the Carnap categoricity of intuitionistic logic can be applied to Prawitz semantics. This implies that Prawitz semantics has a status of its own as a genuine, though incomplete, semantics of intuitionstic logic. An interesting side result is the fact that every formula satisfiable in general semantics is satisfiable in an axioms‐only frame (a frame whose atomic systems do not contain proper rules). We draw a parallel between this seemingly paradoxical result and Skolem's paradox in first‐order model theory.

Simplicial models for the epistemic logic of faulty agents

In recent years, several authors have been investigating simplicial models, a model of epistemic logic based on higher dimensional structures called simplicial complexes. In the original formulation of Goubault et al. (Inf Comput 278:104597, 2021. https://doi.org/10.1016/j.ic.2020.104597), simplicial models are always assumed to be pure, meaning that all worlds have the same dimension. This is equivalent to the standard S5n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbf {S5_n}$$\\end{document} semantics of epistemic logic, based on Kripke models. By removing the assumption that models must be pure, we can go beyond the usual Kripke semantics and study epistemic logics where the number of agents participating in a world can vary. This approach has been developed in a number of papers (van Ditmarsch, WoLLIC 2021, pp 31–46, 2021. https://doi.org/10.1007/978-3-030-88853-4_3; Goubault et al. STACS 2022, pp 33:1–33:20, 2022. https://doi.org/10.4230/LIPIcs.STACS.2022.33; Goubault et al. LICS, pp 1–13, 2023. https://doi.org/10.1109/LICS56636.2023.10175737), with applications in fault-tolerant distributed computing where processes may crash during the execution of a system. A difficulty that arises is that subtle design choices in the definition of impure simplicial models can result in different axioms of the resulting logic. In this paper, we classify those design choices systematically, and axiomatize the corresponding logics. We illustrate them via distributed computing examples of synchronous systems where processes may crash.

Simplified Semantics for Further Relevant Logics I

This paper shows that the relevant logics E and Π′ are strongly sound and complete with regards to a version of the “simplified” Routley-Meyer semantics. Such a semantics for E has been thought impossible. Although it is impossible if an admissible rule of E  the rule of restricted assertion or equivalently Ackermann’s δ-rule  is solely added as a primitive rule, it is very much possible when E is axiomatized in the way Anderson and Belnap did. The simplified semantics for E and Π′ requires unreduced frames. Contra what has been claimed, however, no additional frame component is required over and above what’s required to model other relevant logics such as T and R. It is also shown how to modify the tonicity requirements of the ternary relation so as to allow for the standard truth condition for both fusion – the intensional conjunction ◦ – as well as the converse conditional ←.

Intuitionistic S4 as a logic of topological spaces

Abstract We design and study various topological semantics for the diamond-free intuitionistic modal logic $\textsf{iS4}$, an intuitionistic analogue of $\textsf{S4}$. Ultimately we prove that ordinary topological spaces can be used as semantics, using the specialization order to interpret intuitionistic implication and the interior for the modality. Some of our soundness and completeness results are mechanised in Coq.

The Semantics of Stative Locative Events in Vietnamese: A Spatial Exploration

This study utilizes mathematical formalism and Figure-Ground argument mapping to categorize stative locative events in Vietnamese as surjective or bijective. Bijective events exhibit a one-to-one mapping of Figures and Grounds, while surjectives allow a single Figure to map onto multiple Grounds. Through analysis of Vietnamese sentences, the paper demonstrates how bijective and surjective locatives encode deterministic and ambiguous spatial relations between Figures and Grounds, respectively. This novel distinction aids in enhancing the understanding of locative event typologies and provides an explanatory model for cross-linguistic analysis. The proposed integrated formal framework combines predicate logic, set theory, and lexical semantics to account for complex locative meanings, with significant applications in computational and theoretical linguistics, as well as cognitive science.

Free Constructions in Hoops via $$\ell $$-Groups

AbstractLattice-ordered abelian groups, or abelian$$\ell $$ ℓ -groups in what follows, are categorically equivalent to two classes of 0-bounded hoops that are relevant in the realm of the equivalent algebraic semantics of many-valued logics: liftings of cancellative hoops and perfect MV-algebras. The former generate the variety of product algebras, and the latter the subvariety of MV-algebras generated by perfect MV-algebras, that we shall call $$\textsf{DLMV}$$ DLMV . In this work we focus on these two varieties and their relation to the structures obtained by forgetting the falsum constant 0, i.e., product hoops and DLW-hoops. As main results, we first show a characterization of the free algebras in these two varieties as particular weak Boolean products; then, we show a construction that freely generates a product algebra from a product hoop and a DLMV-algebra from a DLW-hoop. In other words, we exhibit the free functor from the two algebraic categories of hoops to the corresponding categories of 0-bounded algebras. Finally, we use the results obtained to study projective algebras and unification problems in the two varieties (and the corresponding logics); both varieties are shown to have (strong) unitary unification type, and as a consequence they are structurally and universally complete.

Probabilistic Semantics and Calculi for Multi-valued and Paraconsistent Logics

Probabilistic Semantics and Calculi for Multi-valued and Paraconsistent Logics

The Logical Semantics of Conjunctions in Kurdish Language

The Logical Semantics of Conjunctions in Kurdish Language

A correspondence theorem for interpretability logic with respect to Verbrugge semantics

Abstract Interpretability logic is a modal logic that can be used to describe relative interpretability between extensions of a given first-order arithmetical theory. Verbrugge semantics is a generalization of the basic semantics for interpretability logic. Bisimulation is the basic equivalence between models for modal logic. The Van Benthem Correspondence Theorem establishes modal logic as the bisimulation invariant fragment of first-order logic. In this paper we show that a special type of bisimulations, the so-called w-bisimulations, enable an analogue of the Van Benthem Theorem for interpretability logic w.r.t. Verbrugge semantics.

Cognitive Thinking Differences in E-C Translation Driven by Temporal/Spatial Preferences: A Case Study of the Translation of “The Proceedings of the International Military Tribunal for the Far East”

This study, grounded in the interdisciplinary integration of cognitive science and translation studies known as translation cognition, examines how differing temporal-spatial cognitive orientations in English and Chinese influence translation processes. English exhibits a temporality preference, explicitly linking semantic logic through grammatical and lexical devices, while Chinese demonstrates a spatiality preference with nonlinear, chunked, and discrete language encoding. During translation, translators must cognitively reconstruct the source language to align with the target language's cognitive and expressive conventions. Analyzing English-Chinese translation cases from "The Proceedings of the International Military Tribunal For the Far East," the research reveals cognitive strategies in semantic processing and sentence restructuring. It emphasizes the importance of understanding and applying temporal-spatial cognitive differences in cross-linguistic and cross-cultural communication.

From GTC to : Generating reset proof systems from cyclic proof systems

We consider cyclic proof systems in which derivations are graphs rather than trees. Such systems typically come with a condition that isolates which derivations are admitted as proofs, known as the soundness condition. This soundness condition frequently takes the form of either a global trace condition, a property dependent on all infinite paths in the proof-graph, or a reset condition, a ‘local’ condition depending on the simple cycles only which, as a result, is typically stable under more proof transformations.In this article we present a general method for constructing cyclic proof systems with reset conditions from systems with global trace conditions. In contrast to previous approaches, this method of generation is entirely independent of logic's semantics, only relying on combinatorial aspects of the notion of ‘trace’ and ‘progress’. We apply this method to present reset proof systems for three cyclic proof systems from the literature: cyclic arithmetic, cyclic Gödel's T and cyclic tableaux for the modal μ-calculus.