Semantics Of Logic Research Articles

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

A New Game Theoretic Semantics (GTS-2) for Weak Kleene Logics

AbstractHintikka’s game theoretical approach to semantics has been successfully applied also to some non-classical logics. A recent example is Başkent (A game theoretical semantics for logics of nonsense, 2020. arXiv:2009.10878), where a game theoretical semantics based on three players and the notion of dominant winning strategy is devised to fit both Bochvar and Halldén’s logics of nonsense, which represent two basic systems of the family of weak Kleene logics. In this paper, we present and discuss a new game theoretic semantics for Bochvar and Halldén’s logics, GTS-2, and show how it generalizes to a broader family of logics of variable inclusions.

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.

Analysis of Ambiguity, Vagueness, Fuzziness, Uncertainty, Possibility and Probability in the Natural Language Semantics with Fuzzy Logic

Understanding the esotericism of human instinct in their daily life conversation is not enough then a mystery now. This is a bundle of ambiguity, vagueness, fuzziness, uncertainty, possibility and probability as a wrap that humans have built around themselves. With the advancement in artificial Intelligence, natural language processing is more capable now to work with real world and performing intelligent analysises. The real world has interactions between natural and artificial intelligent systems. Despite all it, humans retained their superiority over artificial intelligent systems. The fuzzy Logic can play an important computational role in understanding this intelligence gap in clear dimensions. Logical Semantics, Distributional Semantics and Probabilistic Logic are focused on their intention for better natural language semantic representations. But no single semantic representation fulfills all requirements needed for a satisfactory representation. The objective of the present work has two folds. The first one focused on the understanding of fuzzy logic in two dimensions as an intelligence computational technique and another as mathematical modeling of natural language semantics. The second fold illustrates this intelligence gap with real world examples of natural language processing applications such as Google and Microsoft Translator.

Fast computation of General SimRank on heterogeneous information network

Similarity computation is a fundamental aspect of information network analysis, underpinning many research tasks including information retrieval, clustering, and recommendation systems. General SimRank (GSR), an extension of the well-known SimRank algorithm, effectively computes link-based global similarities incorporating semantic logic within heterogeneous information networks (HINs). However, GSR inherits the recursive nature of SimRank, making it computationally expensive to achieve convergence through iterative processes. While numerous rapid computation methods exist for SimRank, their direct application to GSR is impeded by differences in their underlying equations. To accelerate GSR computation, we introduce a novel approach based on linear systems. Specifically, we transform the pairwise surfer model of GSR on HINs into a new random walk model on a node-pair graph, establishing an equivalent linear system for GSR. We then develop a fast algorithm utilizing the local push technique to compute all-pair GSR scores with guaranteed accuracy. Additionally, we adapt the local push method for dynamic HINs and introduce a corresponding incremental algorithm. Experimental results on various real datasets demonstrate that our algorithms significantly outperform the traditional power method in both static and dynamic HIN contexts.

Categorical Proof-theoretic Semantics

AbstractIn proof-theoretic semantics, model-theoretic validity is replaced by proof-theoretic validity. Validity of formulae is defined inductively from a base giving the validity of atoms using inductive clauses derived from proof-theoretic rules. A key aim is to show completeness of the proof rules without any requirement for formal models. Establishing this for propositional intuitionistic logic raises some technical and conceptual issues. We relate Sandqvist’s (complete) base-extension semantics of intuitionistic propositional logic to categorical proof theory in presheaves, reconstructing categorically the soundness and completeness arguments, thereby demonstrating the naturality of Sandqvist’s constructions. This naturality includes Sandqvist’s treatment of disjunction that is based on its second-order or elimination-rule presentation. These constructions embody not just validity, but certain forms of objects of justifications. This analysis is taken a step further by showing that from the perspective of validity, Sandqvist’s semantics can also be viewed as the natural disjunction in a category of sheaves.

Attack principles in sequent-based argumentation theory

Abstract Attack principles have been introduced in semi-abstract argumentation frameworks and, in the present work, we interpret them in sequent-based argumentation frameworks. Thus, we investigate the role of minimality and consistency of the support set of an argument. Through the notion of preservation of strength, we introduce a formal criterion to sort out the attack principles; isolate the more “acceptable” ones, i.e. those easier to justify; and recover a new argumentative semantics for the non-classical logic that arises from dropping the rules $(\neg , r)$, $(\land , r)$ and $(\supset , l)$ from Gentzen’s classical sequent calculus for classical logic $\textsf{LK}$.

Living and dying on the edge in the digital age. An interview with Andrei Vieru on why closure and boundaries matter in science, art, and life

ABSTRACT 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.