Theoretic Semantics Research Articles

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.

CORRELATION OF THE TERMS "CLASSIFICATION ATTRIBUTE", "MOTIVATIONAL ATTRIBUTE", "SEMANTIC ATTRIBUTE"

The problem of distinguishing the terms "classification attribute", "motivational attribute", "semantic attribute" arose in connection with the active development of cognitive linguistics and the expansion of its terminology. The article describes for the first time approaches to understanding terms in a comparative aspect. The author analyzes dictionary definitions, consistently identifying classification, motivational, semantic features of lexemes, demonstrating the differences between these features. The author comes to the conclusion that the terms "classification attribute", "motivational attribute", "semantic attribute" differ functionally, their use is due to the paradigm and the field of linguistics in which the researcher works. Purpose. The purpose of the study is to distinguish the terms "classification attribute", "motivational attribute", "semantic attribute". Materials and methods. The material for the study was contexts with these terms extracted from scientific papers on cognitive linguistics, word formation, theoretical semantics, as well as dictionary entries. The descriptive and comparative methods, and method of theoretical analysis, were used. Results. The results of the study showed that the terms "motivational attribute", "semantic attribute", "classification attribute" differ functionally. The study of motivational attribute is aimed at identifying linguistic patterns. The study of semantic attribute is aimed at describing lexical (linguistic) meanings. The analysis of classification attribute aims to identify extralinguistic, namely cognitively significant information about the objects of reality. Practical implications. The results of the study can be used in lexicographic and translation practice, in research on issues of nomination, lexical meaning and linguistic categorization.

DEVELOPMENT OF AN ONTOLOGICAL MODEL OF DEEP LEARNING NEURAL NETWORKS

This research paper examines the challenges and prospects associated with the integration of artificial neural networks and knowledge bases. The focus is on leveraging this integration to address practical problems. The paper explores the development, training, and integration of artificial neural net- works, emphasizing their adaptation to knowledge bases. This adaptation involves processes such as in- tegration, communication, representation of ontological structures, and interpretation by the knowledge base of the artificial neural network's representation through input and output. The paper also delves into the direction of establishing an intellectual environment conducive to the development, training, and integration of adapted artificial neural networks with knowledge bases. The knowledge base embedded in an artificial neural network is constructed using a homogeneous semantic network, and knowledge processing employs a multi-agent approach. The representation of artificial neural networks and their specifications within a unified semantic model of knowledge representation is detailed, encompassing text-based specifications in the language of knowledge representation with theoretical semantics. The models shared with the knowledge base include dynamic and other types that vary in their capabilities for knowledge representation. Furthermore, the paper conducts an analysis of approaches to creating artificial neural networks across various libraries of the high-level programming language Python. It explores techniques for developing arti- ficial neural networks within the Python development environment, investigating the key features and func- tions of these libraries. A comparative analysis of neural networks created in object-oriented programming languages is provided, along with the development of an ontological model for deep learning neural net- works.

Монадные вычисления в теоретико-типовой семантике

Monad is a construction from the category theory, which could be understood as an abstraction of computation [Moggi, 1991]. This is a computation resulting not simply in the computed value but in this value with an additional structure. In recent years, monad in this sense has been successfully applied to natural language semantics in the framework of Montague’s formalism. This article deals with monad computation applications in type theoretical semantics [Ranta, 1994]. Several examples illustrate the usage of monads as well as applicative functors for contexts accounting in various situations, controlling the order of quantifiers, belief reports formalization. The language of formalization is Agda

Dual forgetting operators in the context of weakest sufficient and strongest necessary conditions

Forgetting is an important concept in knowledge representation and automated reasoning with widespread applications across a number of disciplines. A standard forgetting operator, characterized in [26] in terms of model-theoretic semantics and primarily focusing on the propositional case, opened up a new research subarea. In this paper, a new operator called weak forgetting, dual to standard forgetting, is introduced and both together are shown to offer a new more uniform perspective on forgetting operators in general. Both the weak and standard forgetting operators are characterized in terms of entailment and inference, rather than a model theoretic semantics. This naturally leads to a useful algorithmic perspective based on quantifier elimination and the use of Ackermann's Lemma and its fixpoint generalization. The strong formal relationship between standard forgetting and strongest necessary conditions and weak forgetting and weakest sufficient conditions is also characterized quite naturally through the entailment-based, inferential perspective used. The framework used to characterize the dual forgetting operators is also generalized to the first-order case and includes useful algorithms for computing first-order forgetting operators in special cases. Practical examples are also included to show the importance of both weak and standard forgetting in modeling and representation.

The Epistemology of Nondeterminism

This paper proposes new semantics for propositional dynamic logic (PDL), replacing the standard relational semantics. Under these new semantics, program execution is represented as fundamentally deterministic (i.e., functional), while nondeterminism emerges as an epistemic relationship between the agent and the system: intuitively, the nondeterministic outcomes of a given process are precisely those that cannot be ruled out in advance. We formalize these notions using topology and the framework of dynamic topological logic (DTL) (Kremer and Mints in Ann Pure Appl Logic 131:133–158, 2005). We show that DTL can be used to interpret the language of PDL in a manner that captures the intuition above, and moreover that continuous functions in this setting correspond exactly to deterministic processes. We also prove that certain axiomatizations of PDL remain sound and complete with respect to the corresponding classes of dynamic topological models. Finally, we extend the framework to incorporate knowledge using the machinery of subset space logic (Dabrowski et al. in Ann Pure Appl Logic 78:73–110, 1996), and show that the topological interpretation of public announcements as given in Bjorndahl (in: van Ditmarsch and Sandu (eds) Jaakko Hintikka on knowledge and game theoretical semantics, outstanding contributions to Logic, vol 12, Springer, 2018) coincides exactly with a natural interpretation of test programs.

VSE-TAKI AS A MARKER OF MONOLOGICAL DISCOURSE CONTRADICTION

Background. The research was carried out within the project «Oral history of Irkutsk and technologies oral history in an interdisciplinary perspective». An analysis of the array of in-depth interviews obtained during the implementation of the project reveals a significant number of fragments reflecting the internal conflict of the speaker’s ideas about some fragment of the real world, which is in the center of his attention at a certain moment of speech. A current issue is to identify linguistic and discourse markers that objectify the presence of this conflict. One of these markers is vse-taki to which the article is devoted.
 The purpose of the work is to clarify the idea of the status of this unit, its semantic, pragmatic and functional features, based on the understanding of the existing lexicographic tradition and the analysis of empirical material.
 The material of the research is the data of traditional explanatory dictionaries and the Active dictionary of the Russian language, as well as examples of contextual use of vse-taki, extracted from the RNC. Methods and techniques of definitional, structural-semantic, contextual and corpus analysis are used.
 The results of the research showed that vse-taki should be qualified as a particle which is used (a) as a marker of the opposition of the existing state of affairs to a hypothetical, but more standard one; (b) as a marker of the reason for the implementation of one of the two alternatives; (c) as a marker of the speaker’s emotional reaction to the coincidence of fragments of the mental and real world.
 The field of practical implications of the results is theoretical semantics and discourse analysis (including in social research). The results can be used in semantics, pragmatics, discourse theory university courses.

Силлогистика как логика всех отношений между двумя непустыми множествами

В работе предлагается язык позитивной силлогистики, алфавит которого содержит все силлогистические константы. Сами эти константы понимаются как знаки отношений между двумя непустыми множествами (объемами двух общих терминов). Среди указанных отношений особое место занимают те, которым соответствует в точности одна из пяти диаграмм Эйлера--Жергонна: (1) равенство множеств, (2) строгое включение первого множества во второе, (3) строгое включение второго множества в первое, (4) перекрещивание множеств, (5) несовместимость множеств. Остальные отношения представляют из себя комбинации эйлеровских. Каждая константа $\textit{k}$ в предлагаемом силлогистическом языке кодируется последовательностью чисел от 1 до 5, указывающих на номера тех эйлеровских отношений, при которых простое высказывание форм $\textit{SkP}$ принимает значение <<истина>>. Например, отношение включения одного непустого множества в другое репрезентирует константа 12, а отношение совместимости двух непустых множеств – константа 1234.Задается точная теоретико-множественная семантика данного <<универсального>> языка, соответствующая интуитивному пониманию силлогистических констант. Вводятся понятия выразимости силлогистической константы в <<локальном>> языке, содержащем лишь некоторые из таких констант, и полноты множества исходных констант некоторого <<локального>> языка. Константа $k$ выразима в локальном силлогистическом языке с неким набором исходных силлогистических констант, если и только если в этом локальном языке найдется формула $A$, содержащая в точности два термина $S$ и $P$, такая что $A$ эквивалентна формуле $SkP$ в семантике универсального силлогистического языка. Множество силлогистических констант $\{k_1, k_2,..., k_m\}$ называется $\textit{полным}$, если и только если любая силлогистическая константа выразима в языке с исходными силлогистическими константами $k_1$, $k_2$,..., $k_m$. В качестве примера доказывается полнота множества исходных констант традиционной силлогистики ($\textit{a}$, $\textit{e}$, $\textit{i}$, $\textit{o}$) и множества исходных констант силлогистики Венна (знаков пяти эйлеровских отношений). В универсальном силлогистическом языке строится аксиоматическое исчисление, доказываются метатеоремы о его непротиворечивости и полноте.

A Game Theoretical Semantics for Logics of Nonsense

Logics of non-sense allow a third truth value to express propositions that are \emph{nonsense}. These logics are ideal formalisms to understand how errors are handled in programs and how they propagate throughout the programs once they appear. In this paper, we give a Hintikkan game semantics for logics of non-sense and prove its correctness. We also discuss how a known solution method in game theory, the iterated elimination of strictly dominated strategies, relates to semantic games for logics of nonsense. Finally, we extend the logics of nonsense only by means of semantic games, developing a new logic of nonsense, and propose a new game semantics for Priest's Logic of Paradox.

To Believe in the Old Church Slavonic Gospel Translation (Codex Marianus)

Drawing on theoretical definition of a speech act, the paper seeks to compare the theoretical semantics of BELIEVE with the lexical semantics of the words used in the Old Slavonic Gospel translation for expressing different modes of believing. The general principles in the use of the verb веровати and related paraphrasing utterances in comparison to Greek according to the majority of instances have been considered. The historical use of lexical material shows that the development of different ways of morphosyntactic use reflects the development of communication practices which are an index of societal behaviour. The author states it that the comparison of the speech act BELIEVE with contested lexical semantics provided the conclusion that a verb *věriti cannot be reconstructed for Proto-Slavic, but at the period under analysis the concept BELIEVE was verbalized by веровати with the primary personal meaning of "believe in someone" (the dative of a person is needed in constructions like "I have faith in Him"). It is supposed that the necessity to introduce the verb *věriti appeared when people started to extend the personal meaning of BELIEVE upto "an impersonal believed object" (sematic bleaching), and if they did it the verb *věriti might had been analogically produced as derivation of the primary noun. The author concludes that the translation technique of the first Slavonic Bible is more ad sensum than ad verbum and sometimes even reveals theological considerations of the translator. The speech act BELIEVE seems to display semantic bleaching as it loses its transcendent truth conditions and becomes more and more connected with impersonal believed objects.

Gestural Cosuppositions within the Transparency Theory

Gestural Cosuppositions within the Transparency Theory

About effective versions of game theoretical semantics for first-order logic

About effective versions of game theoretical semantics for first-order logic

A generalised quantifier theory of natural language in categorical compositional distributional semantics with bialgebras

AbstractCategorical compositional distributional semantics is a model of natural language; it combines the statistical vector space models of words with the compositional models of grammar. We formalise in this model the generalised quantifier theory of natural language, due to Barwise and Cooper. The underlying setting is a compact closed category with bialgebras. We start from a generative grammar formalisation and develop an abstract categorical compositional semantics for it, and then instantiate the abstract setting to sets and relations and to finite-dimensional vector spaces and linear maps. We prove the equivalence of the relational instantiation to the truth theoretic semantics of generalised quantifiers. The vector space instantiation formalises the statistical usages of words and enables us to, for the first time, reason about quantified phrases and sentences compositionally in distributional semantics.

Enabling metrology-oriented specification of geometrical variability – A categorical approach

In this paper a metrology-oriented specification schema is proposed to enrich the specification semantics with sufficient metrological information. It is designed particularly for applications where non-traditional measurement methods are applied; and it can also identify any redundancies, inconsistencies or incompletenesses of a specification. The proposed schema is based on category theoretical semantics which uses category theory as the foundation to model the semantics. A set of verification operations that derived from the measurement process was firstly formalised using the categorical semantics. Then a set of full faithful functors were constructed to map the set of verification operations to a set of specification operations. A set of simplification rules was then developed to deduce all of the necessary specification objects which are independent to each other. Then the residual specification objects provide a compact structure of the specification. Three test cases were conducted to validate the proposed schema. An industrial computed tomography (CT) measurement process for an impeller manufacturing using selective laser sintering (SLS) technique, was modelled and a set of independent specification elements was then deduced. The other two test cases for checking redundancy and incompleteness on general ISO specifications were carried out. The results show that the proposed schema works for proposing semantic enriched specification that are characterised by non-traditional measurement methods and for testing redundancy and incompleteness of specifications based on geometrical product specifications and verification (GPS) standards system.

A game theoretical semantics for a logic of formal inconsistency

Abstract This paper introduces a game theoretical semantics for a particular logic of formal inconsistency called mbC.

The Thought Uniqueness Hypothesis

A novel principle, the Thought Uniqueness Hypothesis (TUH), unifies several restrictions on interpretation that work in theoretical semantics has observed, in particular the following: binding and scope economy of Fox (2000, MIT Press), and constraints on types (Heim 2017, unpublished; Hirsch 2017, MIT Dissertation). The principle not only derives these phenomena, but makes additional novel pre- dictions such as a reduction of superiority and D-linking data and the interaction of i-within-i phenomena with coordination. Furthermore the principle exhibits close similarities to current work on exhaustification and efficiency (Meyer 2013, MIT Dissertation) with a potential for further unification. The statement of the TUH is most natural on a realizational view of grammar, where conceptual representations are generated by a non-linguistic system, and then realized by the linguistic sys- tem. It therefore argues against the view that surface word order plays a role in interpretation (Chomsky 1970, TEC Co., and others).

Denotational semantics of recursive types in synthetic guarded domain theory

Just like any other branch of mathematics, denotational semantics of programming languages should be formalised in type theory, but adapting traditional domain theoretic semantics, as originally formulated in classical set theory to type theory has proven challenging. This paper is part of a project on formulating denotational semantics in type theories with guarded recursion. This should have the benefit of not only giving simpler semantics and proofs of properties such as adequacy, but also hopefully in the future to scale to languages with advanced features, such as general references, outside the reach of traditional domain theoretic techniques.Working inGuarded Dependent Type Theory(GDTT), we develop denotational semantics for Fixed Point Calculus (FPC), the simply typed lambda calculus extended with recursive types, modelling the recursive types of FPC using the guarded recursive types ofGDTT. We prove soundness and computational adequacy of the model inGDTTusing a logical relation between syntax and semantics constructed also using guarded recursive types. The denotational semantics is intensional in the sense that it counts the number of unfold-fold reductions needed to compute the value of a term, but we construct a relation relating the denotations of extensionally equal terms, i.e., pairs of terms that compute the same value in a different number of steps. Finally, we show how the denotational semantics of terms can be executed inside type theory and prove that executing the denotation of a boolean term computes the same value as the operational semantics of FPC.

Семантика для гиперклассической логики и проблема отрицания в формальном языке

The application of game-theoretic semantics for first-order logic is based on a certain kind of semantic assumptions, directly related to the asymmetry of the definition of truth and lies as the winning strategies of the Verifier (Abelard) and the Counterfeiter (Eloise). This asymmetry becomes apparent when applying GTS to IFL. The legitimacy of applying GTS when it is transferred to IFL is based on the adequacy of GTS for FOL. But this circumstance is not a reason to believe that one can hope for the same adequacy in the case of IFL. Then the question arises if GTS is a natural semantics for IFL. Apparently, the intuitive understanding of negation in natural language can be explicated in formal languages in various ways, and the result of an incomplete grasp of the concept in these languages can be considered a certain kind of anomalies, in view of the apparent simplicity of the explicated concept. Comparison of the theoretical-model and game theoretic semantics in application to two kinds of language – the first-order language and friendly-independent logic – allows to discover the causes of the anomaly and outline ways to overcome it.

The ecological semantics of the IoMT: Modelling cyborgs networks for health policy

Abstract The paper presents an application of the Internet of Medical Things (IoMT) to health policy, particularly to the management of electronic medical records (EMR) for epidemiological surveillance. It develops a game theoretical semantics (GTS) approach for the study of a cyborg's behavior in the context of health policy. The article also analyzes cyborg network dynamics, and presents a system dynamics simulation of the game theory model applied to this theoretical case. The model shows that under certain conditions, cyborg networks can be useful in preventing pandemic results.

Yoad Winter’s Elements of Formal Semantics, 2016, Edinburgh Advanced Textbooks in Linguistics (Edinburgh University Press)

Elements of Formal Semantics (EFS) has already been reviewed twice (Rett in Glossa 1(1):42, 2016; Erlewine in Comput Linguist 42(4):837–839, 2017). As well, the website for the work is accompanied by evaluative quotes by noted scholars. All are very positive concerning its clarity and its utility as an introduction to formal semantics for natural language. As I agree with these evaluations my interest in reiterating them in slightly different words is limited. So my reviews of the content chapters will be accompanied by a Reflections section consisting of my own reflections on the foundations of model theoretic semantics for natural language as laid out in EFS. The issues I address—alternate ways of accomplishing the tasks Winter treats—should not be included in an introductory work but they may be helpful for those who teach classes for which EFS is an appropriate text. They might also help with queries about the content of the text by those using it. I note that a mark of a clear text is that it allows the reader to reflect on its content not its presentation.