Truth, Logical Structure, and Compositionality

This chapter gives a general characterization of the notion of logical form in the light of the truth-theoretic, and then generalized fulfillment-theoretic, approach to natural language semantics. The chapter takes logical form to be semantic form. It explicates the notion of sameness of logical form by making use of the idea of corresponding canonical proofs of appropriate theorems for the sentences in interpretive truth or fulfillment theories for their languages. The chapter discusses also briefly the issue of the identification of logical constants in the language in the light of the semantic framework it employs, and some issues having to do with the extension of the notion of logical validity and logical consequence to natural languages.

The key note of the following remarks will be the distinction between two kinds of attitudes towards the relations between syntax and semantics, which I shall call without any claim to historical accuracy the Fregean and the Russellian attitudes, respectively. My main point will be that as far as the formal analysis of natural languages is concerned, the trend in recent years has been contrary to what Hintikka would have us believe towards more Fregean approaches. By naming them thus I by no means want to imply that these two important precursors of contemporary research in the philosophy of language and linguistic semantics would agree with most of what I will attribute to them. The distinction I want to draw does, however, cut across many of the issues dealt with in Hintikka's paper; to some of these I will turn shortly. But I would first like to motivate the distinction and to argue briefly for one of the two. The Fregean and Russellian attitudes are essentially alternatives to ways of considering the relation between syntax and semantics within one's theory of language. The Fregean attitude consists in regarding the relation between entities from the two domains as roughly one-to-one. What it basically entails is that the syntactic decomposition of the expressions of the language must enter directly into the semantic computation. A Fregean analysis is typically surface oriented and forsees in general for each syntactic category of the language (or rather of the syntax) a corresponding semantic category. On the other hand, what I am calling the Russellian attitude towards the relation between syntax and semantics is based on the view that the direct surface structure of a language (here I am of course referring to natural languages) is not a faithful guide to its semantic structure, or if you want, to its logical form. Typically, a Russellian attitude will lead to a kind of "syntactic transformationalism", best known, for example, from the kind of work done within the various trends of generative trans formational grammar (where the motivation for transformational analyses was of course not explicitly semantic). One could cite among

The validity of some inferences is said to be explained by reference to the meanings of the particular expressions occurring in them, while that of other inferences is due, rather, to the way in which the sentences are constructed out of their parts. The inference from ‘John knows that snow is white’ to ‘Snow is white’ is given as an example of the first type of inference; for it is said to be explained by providing an analysis of the semantical primitive ‘knows’. The inferences from ‘John ran breathlessly’ to ‘John ran’ and from ‘John is a large man’ to ‘John is a man’ may, tentatively, be taken to be examples of the second type.

The emergence of a fractal structure of formal logic via the spatiotemporal reflexive self-identification

Studying the "quantum logic", one could observe that logical structures, like a language with its syntax and semantics, a consequence operation, etc., can be directly extracted from quantum theory. This way of constructing a language has no precedent in the history of formal logic. The procedure of "taking a well-known physical theory and distilling its logic", as Finkelstein [5] calls it, seems now to be sufficiently developed to apply it beyond the scope of quantum mechanics. The main characteristic feature of this procedure is that, roughly speaking, it reconstructs a syntax from a semantics: we identify some semantical objects within quantum theory, and infer the syntax of the corresponding language. It is the reverse of the common trends in formal logic, where we look for a semantics of a given syntactical structure. The main concern of this work is to find, in the "quantum-logical" manner, languages related to a "mini-theory" of similarity. It seems to be the first application of the quantum "reading off" procedure to a nonquantum theory.' We are still close to the quantum case, as a special similarity structure underlies quantum theory, too. Our considerations can be thus seen as a test of the quantum "reading off" procedure. This study of logical aspects of the notion of similarity is also of interest because this notion appears in some variants of the Kripkian modal semantics.2 After introducing basic notions of the "mini-theory" of similarity and illustrating them by examples (Section 2), we discuss in Section 3 the problem of determining a similarity structure by a set of properties. It is demonstrated that one must use vague properties to do this. This result is of crucial importance; because of it the languages of similarity we obtain have to be multi-valued. A set of objects with a similarity relation over it, together with the set of properties determining this similarity, form a structure resembling to some extent the basic structure of quantum theory. It makes it possible to apply here the same procedure as in the quantum case in order to find a language of the similarity "theory".

This paper presents a logic of questions developed as an extension of (S5) epistemic logic. We discuss many features that are important for erotetic logic (formalization and semantics of questions, answerhood conditions, and inferential structures with questions). The aim is to introduce an erotetic system which corresponds well with epistemic terms and can form an appropriate background for dynamic approaches in epistemic logic.

This article presents a motif index, compiled by the author, for Russian mythological prose, specifically focusing on its Siberian variant. The index is dedicated to the motif of the “mythical master of the peasant house and homestead”. The relevance of this work is underscored by its contribution to the scholarly series “Monuments of Folklore of the Peoples of Siberia and the Far East”, published by the Institute of Philology of the Siberian Branch of the Russian Academy of Sciences in Novosibirsk. The index operates on several key principles. First, a motif is defined as a cohesive unit of logical and semantic structures, representing an abstract concept independent of a specific narrative. Second, motif variability is illustrated by showcasing the variability within its components. Third, the system is designed to accommodate new material. Finally, the index functions as a critical research tool. The index employs the theme as its unit of classification and the motif as its unit of systematization. It is emphasized that creating such an index requires a substantial corpus of texts, relevant experience, and deep immersion in the material, with the researcher’s scholarly intuition also deemed important. Following these principles, the index identifies sixteen motifs, each with a detailed description and explanation of the principles behind its identification and structure. This index facilitates the study of mythological themes, offers an open-ended structure, and provides folklorists with a tool for systematically organizing their regional data.

Drawing on the theoretical lens of intertextuality and employing the Latent Dirichlet Allocation (LDA) topic model, this study systematically examines the similarities and differences between Chinese and American science education policies across three comparative dimensions: (1) structural differences in policy design; (2) similarities and divergences in thematic emphasis; and (3) evolutionary trends in policy agendas. The selection of policy texts followed clear criteria: (1) documents must be issued at the national level (central government in China and federal government in the United States); (2) they must be directly related to science education; and (3) local and informal texts were excluded. A total of 23 policy documents were retained, amounting to approximately 200,000 words. The optimal number of topics was set at four for each country, with coherence scores of 0.75 (China) and 3.70 (United States), ensuring model validity. The results indicate a clear divergence in governance logic and semantic structure between the two countries. In terms of topic structure, Chinese policies exhibit a “one-core, multiple-supports” configuration, with state authority at the semantic center and various social actors functioning as collaborative agents, whereas American policies present a “multi-actor co-construction” pattern in which diverse policy texts resonate horizontally. In terms of topic emphasis, both countries display sustained reinforcement of teacher development, forming a shared policy consensus. In terms of topic evolution, China follows a pattern of linear inheritance, continuously assimilating and layering upon existing policy frameworks, while the United States demonstrates semantic migration, with policy meanings shifting through the reconfiguration of key concepts and ideas. As two representative models of education governance, how China and the United States navigate strategic absorption and reciprocal borrowing within their distinct historical, cultural, and institutional contexts holds significant implications for advancing global science education policy from a phase of parallel development to one of mutual innovation.

Donald Davidson (1984g) famously proposed that what we want from a theory of meaning we may get from a theory of truth. What we want from a theory of meaning for a natural language, that being the case at issue, includes at least an account of the phenomena that give rise to the principle of compositionality: We want an explanation of how the meaning of a complex expression, such as a sentence, depends upon and is determined by the meanings of its syntactic parts. One central advantage of Davidson’s proposal, as he saw it, is that we know from the work of Tarski (1958) how to construct theories of truth for languages with certain sorts of structures, and such a theory does help us to understand how at least some of the semantic properties of complex expressions are determined by those of their parts. Davidson’s practice suggests he may have hoped that all sentences of natural language could be assigned logical forms of the variety familiar from mathematical logic. If so, then semantics would all but reduce to syntax: The only outstanding problem would be to uncover the ‘logical forms’ of the sentences of, say, English. This hope does not now seem reasonable. But the methods available for investigating logical form—that is, for investigating syntax—have become so powerful that it is not at all unreasonable to suppose that the syntactic part of the problem is solvable, at least in principle, and Tarski’s work can be adapted to many of the resulting structures. The work that is left for the semanticist proper then becomes to solve the problems syntax and Tarski do not solve: These include, for example, discovering what sorts of semantic values need to be assigned to novel semantic primitives, such as mass terms, and explaining the semantic significance of novel modes of composition, such as [V PV [CPS]]. It is unfortunate that a proposal with such great advantages faces such grave difficulties. Indeed, it is probably fair to say that most philosophers of language, and perhaps even most working semanticists, regard truththeoretic semantics as a non-starter, for the simple reason that it seems to have the wrong subject-matter. We will not get what we want from a theory of meaning from any theory that does not specify meanings: No theory that does not specify what the sentence ‘snow is white’ means, for example, can possibly explain how this sentence’s meaning what it does is determined by its parts’ meaning what they do. But a theory of truth for English does not specify what even one sentence of English means, since any such theory is consistent with infinitely many different suppositions concerning what any sentence of English means. For example, a theory of truth that proves this T-sentence2 for ‘snow is white’:

One of the main problems in representing information in the form of nonsystematic logic is the lack of flexibility, which leads to potential overfitting. Although nonsystematic logic improves the representation of the conventional k Satisfiability, the formulations of the first, second, and third-order logical structures are very predictable. This paper proposed a novel higher-order logical structure, named G-Type Random k Satisfiability, by capitalizing the new random feature of the first, second, and third-order clauses. The proposed logic was implemented into the Discrete Hopfield Neural Network as a symbolic logical rule. The proposed logic in Discrete Hopfield Neural Networks was evaluated using different parameter settings, such as different orders of clauses, different proportions between positive and negative literals, relaxation, and differing numbers of learning trials. Each evaluation utilized various performance metrics, such as learning error, testing error, weight error, energy analysis, and similarity analysis. In addition, the flexibility of the proposed logic was compared with current state-of-the-art logic rules. Based on the simulation, the proposed logic was reported to be more flexible, and produced higher solution diversity.

An integration of deep learning and symbolic logic is proposed, based on the Curry-Howard isomorphism and categorical logic. The propositional structure of logic is seen as a symmetry, namely the permutation invariance of propositions; This can be implemented using so-called symmetric neural networks. Under our interpretation, it turns out that Google’s BERT, which many currently state-of-the-art language models are derived from, can be regarded as an alternative form of logic. This BERT-like structure can be incorporated under a reinforcement-learning framework to form a minimal AGI architecture. We also mention some insights gleaned from category and topos theory that point to future directions and may be helpful to other researchers, including mathematicians interested in AGI.KeywordsDeep learningSymbolic logicLogic-based AINeural-symbolic integrationCurry-Howard isomorphismCategory theoryTopos theoryFuzzy logic

The Logical Positivists’ theory of truth developed step by step from a correspondence-theory into a restrained coherence theory. The philosophical ideas which L. Wittgenstein has developed in his Tractatus Logico-Philosophicus, and which represent the logical and historical starting point of the Viennese Circle’s researches, are obviously characterized by a correspondence theory of truth. The logical form in which a molecular statement is constituted by atomic ones reflects the formal structure of facts; and, consequently, just as the existence or non-existence of a molecular fact is determined by the existence or non-existence of its atomic constituents, the truth or falsity of a molecular statement is determined by the corresponding properties of the atomic statements; that is to say: each statement is conceived to be a truth-function of the atomic statements. The evolution of the concept of truth people considered is intimately allied to a change of view concerning the logical function of protocol statements.

The article is a review of the monograph by S.I. Zakhartsev, D.V. Maslennikov, V.P. Salnikov “Logos of Law: Parmenides - Hegel - Dostoevsky. On the Speculative-logical foundations of the Metaphysics of Law” 2019 and its English edition 2021 In the process of analyzing this work, the peculiarity of its authors’ understanding of the subject and method of philosophy as a science of the universal unity of thinking and being, realized in the complementarity of historical and logical forms, is revealed. Based on this, the authors of the monograph largely fill the gap that exists in philosophical and legal knowledge. Namely: they reveal the theoretical content of the process of mediation of general philosophy and Philosophy of Law. In this context, the philosophical and philosophical-legal teachings of Parmenides, Plato, Aristotle, Descartes, Kant, Fichte, Hegel, Dostoevsky are analyzed as necessary steps in the unified process of cognition of the essence and meaning of legal existence. As a result, the authors of the monograph give a modern interpretation of the main problems of the Philosophy of Law: the problems of the absolute in law, the value dimension in law, the relationship of the historical and logical principles of law and legal thinking, time and eternity, and others, as well as lay the foundations of legal Christology, substantiate the model of the comprehensive theory of law.

This handbook provides a systematic survey of the central areas of philosophical logic. It is divided into four volumes, each devoted to a major sub-field within the disciplines. The articles should be of value to general philosophers, linguists, logicians, mathematicians and computer scientists. Volume 1, Elements of Classical Logic, deals with the background to what has come to be considered the standard formulation of predicate logic - both as far as its semantics and proof theory are concerned. The central chapter on predicate logic is followed by chapters outlining various alternative, but essentially equivalent ways of constructing the semantics for first-order logic as well as its proof theory. In addition, this volume contains a discussion of higher-order extensions of first-order logic and a compendium of the algorithmic and decision-theoretic prerequisites in the study of logical systems. Volume 2, Extensions of Classical Logic, surveys the most significant extensions of predicate logic and their applications to various philosophical fields of inquiry. The 12 chapters in this volume together provide a succinct introduction to a variety of intensional frameworks, a discussion of the most well-known logical systems, as well as an overview of major applications and of the open problems in the respective fields. Volume 3, Alternatives to Classical Logic, consists of a series of surveys of some of the alternatives to the basic assumptions of classical logic. These include many-valued logic, partial logic, free logic, relevance and entailment logics, dialogue logic, quantum logic and intuitionism. Volume 4, Topics in the Philosophy of Language, presents a panorama of the applications of logical tools and methods in the formal analysis of natural language. Since a number of developments in philosophical logic were originally stimulated by concern arising in the semantic analysis of natural language discourse, the chapters in this volume provide some criteria of evaluation of the applications of work in philosophical logic. In revealing both the adequacies and inadequacies of logical investigations in the semantic structures of natural discourse, these chapters also point the way to future developments in philosophical logic in general and thus close again the circle of inquiry relating logic and language.

The article examines the linguistic means of representing the subcriminal feature "denial of the armed aggression of the Russian Federation against Ukraine" in anti-state texts on social networks. The study found that the representatives of the "denial of the armed aggression of the Russian Federation against Ukraine" are multilevel linguistic units: the negative prefix not-, in the semantic structure of which denial is part of a complex meaning; the negative particle not, used to completely deny the content of what is said; negative pronouns; and the negative predicate no. The following explicit means of realizing negation are the most productive in conflict texts: 1) general negative logical and syntactic structures with the negative particle not used in preposition to the main predicative member of a two-part sentence; 2) partially negative logical and syntactic structures with the negative particle not used in preposition to the secondary member of a two-part sentence; 3) logical and syntactic structures with the negative predicate no. The logical operation of negation is most productively realized in the implicit form at the level of a whole sentence or microcontext and is actualized through such semantic plans as the interpretation of the armed aggression of the Russian Federation against Ukraine as a special military operation, as an internal civil conflict, as Ukrainian aggression in Donbas, the interpretation of the war as Ukraine's armed aggression, as military exercises, as a war between the United States and Russia, as a war unleashed by a third party, as well as the denial of the armed aggression of the Russian Federation against Ukraine as an unprovoked armed attack by one state against another with the aim of seizing its territory, eliminating or limiting its independence.