A general game player automatically learns to play arbitrary new games solely by being told their rules. For this purpose games are specified in the general Game Description Language (GDL), a variant of Datalog with function symbols that uses a few game-specific keywords. A recent extension of basic GDL allows the description of nondeterministic games with any number of players who may have incomplete, asymmetric information. In this paper, we analyse the epistemic structure and expressiveness of this (...) language in terms of modal epistemic logic and prove two main results: (1) The operational semantics of GDL entails that the situation at any stage of a game can be characterised by a multi-agent epistemic (i.e., S5-) model; (2) GDL is sufficiently expressive to model any situation that can be described by a (finite) multi-agent epistemic model. (shrink)

Qualitative coalitional games (QCGs) were introduced as abstract formal models of goal-oriented cooperative systems. A QCG is a game in which each agent is assumed to have some goal to achieve, and in which agents must typically cooperate with others in order to satisfy their goals. In this paper, we show how it is possible to reason about QCGs using Coalition Logic (CL), a formalism intended to facilitate reasoning about coalitional powers in game-like multiagent systems. We introduce a (...) correspondence relation between QCGs and interpretations for CL, which defines the circumstances under which a CL interpretation correctly characterises a QCG. The complexity of deciding correspondence between QCGs and interpretations for CL is shown to vary from being tractable up to Πp 2-complete, depending on the representation chosen for the QCG and interpretation. We then show how various properties and solution concepts of QCGs can be characterised as CL formula schemes. The ideas are illustrated via a detailed worked example, in which we demonstrate how a model checker can be deployed to investigate whether a particular system has the properties in question. (shrink)

The papers collected in this volume exemplify some of the trends in current approaches to logic, language and computation. Written by authors with varied academic backgrounds, the contributions are intended for an interdisciplinary audience. The first part of this volume addresses issues relevant for multi-agent systems: reasoning with incomplete information, reasoning about knowledge and beliefs, and reasoning about games. Proofs as formal objects form the subject of Part II. Topics covered include: contributions on logical frameworks, linear logic, and different (...) approaches to formalized reasoning. Part III focuses on representations and formal methods in linguistic theory, addressing the areas of comparative and temporal expressions, modal subordination, and compositionality. (shrink)

We describe a fully abstract semantics for a simple functional language with locally declared names which may be used as pointers to names. It is based on a category of dialogue games acted upon by the group of natural number automorphisms. This allows a formal, semantic characterization of the key properties of names such as freshness and locality.We describe a model of the call-by-value λ-calculus based on these games, and show that it can be used to interpret the nu-calculus (...) of Pitts and Stark. We then construct a model of our pointer-language by extending our category of games with an explicit representation of the store, using a notion of semantic garbage-collection to erase inaccessible pointers. Using factorization and decomposition techniques, we show that the compact elements of our model are definable as terms, and hence it is fully abstract. (shrink)

In this article, I present a dynamic logic game for defeasible reasoning. I argue that, as far as defeasible reasoning is concerned, one should distinguish between practical and ideal rationality. Starting from the adaptive logic framework, I formalize both rationality notions by means of logic games. The presented adaptive logic games are based on (i) standard logic games on the one hand and (ii) dynamic proof procedures for adaptive logic on the other hand. The games are similar to standard (...) logic games, but have the extra property that some moves are revisable. This is handled by means of a main control game, which starts different standard logic games. I argue that the adaptive logic games form intuitive reasoning models for rationality in defeasible reasoning contexts. Moreover, I will also demonstrate that the games give a good insight in the computational complexity of defeasible reasoning forms. (shrink)

We combine linear temporal logic (with both past and future modalities) with a deontic version of justification logic to provide a framework for reasoning about time and epistemic and normative reasons. In addition to temporal modalities, the resulting logic contains two kinds of justification assertions: epistemic justification assertions and deontic justification assertions. The former presents justification for the agent’s knowledge and the latter gives reasons for why a proposition is obligatory. We present two kinds of semantics for the logic: one (...) based on Fitting models and the other based on neighborhood models. The use of neighborhood semantics enables us to define the dual of deontic justification assertions properly, which corresponds to a notion of permission in deontic logic. We then establish the soundness and completeness of an axiom system of the logic with respect to these semantics. Further, we formalize the Protagoras versus Euathlus paradox in this logic and present a precise analysis of the paradox, and also briefly discuss Leibniz’s solution. (shrink)

This volume brings together a group of logic-minded philosophers and philosophically oriented logicians, mainly from Asia, to address a variety of logical and philosophical topics of current interest, offering a representative cross-section of the philosophical logic landscape in early 21st-century Asia. It surveys a variety of fields, including modal logic, epistemic logic, formal semantics, decidability and mereology. The book proposes new approaches and constructs more powerful frameworks, such as cover theory, an algebraic approach to cut-elimination, and a Boolean approach (...) to causal discovery, to name but a few. Readers may find a wide range of applications of these original works in current research of philosophical logic, especially in the structural and conceptual analysis of some significant semantic properties and formal systems. The variety of topics and issues discussed here will appeal to readers from a broad spectrum of disciplines, ranging from mathematical/philosophical logic, computing science, cognitive science and artificial intelligence, to linguistics, game theory and beyond. (shrink)

It is a common complaint against moral philosophers that their abstract theorising bears little relation to the practical problems of everyday life. Professor Braithwaite believes that this criticism need not be inevitable. With the help of the Theory of Games he shows how arbitration is possible between two neighbours, a jazz trumpeter and a classical pianist, whose performances are a source of mutual discord. The solution of the problem in the lecture is geometrical, and is based on the formal analogy (...) between the logic of the situation and the geometry of a parabola. But an appendix provides the alternative algebraic treatment of a general two-person collaboration situation. (shrink)

I will show that the semantic structure of a new imperfect-information propositional logic can be described in terms of extensive forms of semantic games. I will discuss some ensuing properties of these games such as imperfect recall, informational consistency, and team playing. Finally, I will suggest a couple of applications that arise in physics, and most notably in quantum theory and quantum logics.

In this paper it is argued that Hintikka's game theoreticalsemantics for Independence Friendly logic does not formalize theintuitions about independent choices; it rather is aformalization of imperfect information. Furthermore it is shownthat the logic has several remarkable properties (e.g.,renaming of bound variables is not allowed). An alternativesemantics is proposed which formalizes intuitions aboutindependence.

It is a common complaint against moral philosophers that their abstract theorising bears little relation to the practical problems of everyday life. Professor Braithwaite believes that this criticism need not be inevitable. With the help of the Theory of Games he shows how arbitration is possible between two neighbours, a jazz trumpeter and a classical pianist, whose performances are a source of mutual discord. The solution of the problem in the lecture is geometrical, and is based on the formal analogy (...) between the logic of the situation and the geometry of a parabola. But an appendix provides the alternative algebraic treatment of a general two-person collaboration situation. (shrink)

We develop a multi-agent deontic action logic to study the logical behaviour of two types of deontic conditionals: (1) conditional obligations, having the form "If group H were to perform action aH, then, in group F's interest, group G ought to perform action aG" and (2) conditional permissions, having the form "If group H were to perform action aH, then, in group F's interest, group G may perform action aG". First, we define a formal language for multi-agent deontic action (...) logic and a class of consequentialist models to interpret the formulas of the language. Second, we define a transformation that converts any strategic game into a consequentialist model. Third, we show that an outcome a* is a Nash equilibrium of a strategic game if and only if a conjunction of certain conditional permissions is true in the consequentialist model that results from the transformation of that strategic game. (shrink)

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

Through a phenomenological study of horse-human relations, this article explores the ways in which, as embodied beings, we live relationally, rather than as separate human identities. Conceptually this challenges oppositional logic and humanist assumptions, but where poststructuralist treatments of these issues tend to remain abstract, this article is concerned with an embodied demonstration of the ways in which we experience a relational or in-between logic in our everyday lives.

In the literature there are at least two main formal structures to deal with situations of interactive epistemology: Kripke models and type spaces. As shown in many papers :149–225, 1999; Battigalli and Siniscalchi in J Econ Theory 106:356–391, 2002; Klein and Pacuit in Stud Log 102:297–319, 2014; Lorini in J Philos Log 42:863–904, 2013), both these frameworks can be used to express epistemic conditions for solution concepts in game theory. The main result of this paper is a formal comparison (...) between the two and a statement of semantic equivalence with respect to two different logical systems: a doxastic logic for belief and an epistemic–doxastic logic for belief and knowledge. Moreover, a sound and complete axiomatization of these logics with respect to the two equivalent Kripke semantics and type spaces semantics is provided. Finally, a probabilistic extension of the result is also presented. A further result of the paper is a study of the relationship between the epistemic–doxastic logic for belief and knowledge and the logic STIT by Belnap and colleagues. (shrink)

Contemporary social science tends to suffer from too many misplaced attempts at mathematical or game-theoretical formulation, and much effort is wasted in either propounding such formulations, or in showing their inanity. Jon Elster does not entirely escape this himself, but Logic and Society is truly remarkable in pointing the way to some possibly very relevant formalizations. These are particularly to be found in the chapter on 'contradictions of society'. There Elster attempts to delineate the properties of certain (...) self-frustrating predicaments of action, and to relate them as well to Hegelian-Marxist conceptions of contradiction. It may be, however, that the relevance of this analysis is restricted to societies whose form of life has become atomistic, and whose members thus function in an individual-calculative way in many spheres of life. But even so, formalizations of the kind Elster provides would be useful in defining one kind of historically evolved society among others. (shrink)

This paper addresses the theoretical notion of a game as it arisesacross scientific inquiries, exploring its uses as a technical andformal asset in logic and science versus an explanatory mechanism. Whilegames comprise a widely used method in a broad intellectual realm(including, but not limited to, philosophy, logic, mathematics,cognitive science, artificial intelligence, computation, linguistics,physics, economics), each discipline advocates its own methodology and aunified understanding is lacking. In the first part of this paper, anumber of game theories in formal studies (...) are critically surveyed. Inthe second part, the doctrine of games as explanations for logic isassessed, and the relevance of a conceptual analysis of games tocognition discussed. It is suggested that the notion of evolution playsa part in the game-theoretic concept of meaning. (shrink)

One of the most expected properties of a logical system is that it can be algebraizable, in the sense that an algebraic counterpart of the deductive machinery could be found. Since the inception of da Costa's paraconsistent calculi, an algebraic equivalent for such systems have been searched. It is known that these systems are non self-extensional (i.e., they do not satisfy the replacement property). More than this, they are not algebraizable in the sense of Blok-Pigozzi. The same negative (...) results hold for several systems of the hierarchy of paraconsistent logics known as Logics of Formal Inconsistency (LFIs). Because of this, these logics are uniquely characterized by semantics of non-deterministic kind. This paper offers a solution for two open problems in the domain of paraconsistency, in particular connected to algebraization of LFIs, by obtaining several LFIs weaker than C1, each of one is algebraizable in the standard Lindenbaum-Tarski's sense by a suitable variety of Boolean algebras extended with operators. This means that such LFIs satisfy the replacement property. The weakest LFI satisfying replacement presented here is called RmbC, which is obtained from the basic LFI called mbC. Some axiomatic extensions of RmbC are also studied, and in addition a neighborhood semantics is defined for such systems. It is shown that RmbC can be defined within the minimal bimodal non-normal logic E+E defined by the fusion of the non-normal modal logic E with itself. Finally, the framework is extended to first-order languages. RQmbC, the quantified extension of RmbC, is shown to be sound and complete w.r.t. BALFI semantics. (shrink)

A combination of epistemic logic and dynamic logic of programs is presented. Although rich enough to formalize some simple game-theoretic scenarios, its axiomatization is problematic as it leads to the paradoxical conclusion that agents are omniscient. A cut-free labelled Gentzen-style proof system is then introduced where knowledge and action, as well as their combinations, are formulated as rules of inference, rather than axioms. This provides a logical framework for reasoning about games in a modular and systematic way, and (...) to give a step-by-step reconstruction of agents omniscience. In particular, its semantic assumptions are made explicit and a possible solution can be found in weakening the properties of the knowledge operator. (shrink)

o formalization of intensional functions was made for the purpose of many-valued interpretation of the belief-operators within the scope of the classical logic system. The first aim of the paper is to present and discuss this rather unknown many-valued construction and its properties. The fact that the manyvaluedness of o systems is purely formal - their characteristic matrices are Boolean - calls for further consideration. Departing from intristic similarities of the tables for the epistemic operators to the information functions (...) we show that o structures may be rewritten as special knowledge representation systems. These systems use 0 and 1 as the only values and are called “epistemic”. Their role for the theory of knowledge information systems may be compared to that of the functionally complete matrices in the class of all logical matrices for a given propositional language. (shrink)

Interpretability logic is a modal formalization of relative interpretability between first‐order arithmetical theories. Verbrugge semantics is a generalization of Veltman semantics, the basic semantics for interpretability logic. Bisimulation is the basic equivalence between models for modal logic. We study various notions of bisimulation between Verbrugge models and develop a new one, which we call w‐bisimulation. We show that the new notion, while keeping the basic property that bisimilarity implies modal equivalence, is weak enough to allow the converse to hold in (...) the finitary case. To do this, we develop and use an appropriate notion of bisimulation games between Verbrugge models. (shrink)

This paper proposes a logical framework for representing static and dynamic properties of different kinds of individual and collective attitudes. A complete axiomatization as well as a decidability result for the logic are given. The logic is applied to game theory by providing a formal analysis of the epistemic conditions of iterated deletion of weakly dominated strategies (IDWDS), or iterated weak dominance for short. The main difference between the analysis of the epistemic conditions of iterated weak dominance (...) given in this paper and other analysis is that we use a semi-qualitative approach to uncertainty based on the notion of plausibility first introduced by Spohn, whereas other analysis are based on a quantitative representation of uncertainty in terms of probabilities. (shrink)

Proof assistants are software-based tools that are used in the mechanization of proof construction and validation in mathematics and computer science, and also in certified program development. Different such tools are being increasingly used in order to accelerate and simplify proof checking, and the Coq proof assistant is one of the most well known and used in large-scale projects. Language and automata theory is a well-established area of mathematics, relevant to computer science foundations and information technology. In particular, context-free language (...) theory is of fundamental importance in the analysis, design, and implementation of computer programming languages. This work describes a formalization effort, using the Coq proof assistant, of fundamental results of the classical theory of contextfree grammars and languages. These include closure properties (union, concatenation, and Kleene star), grammar simplification (elimination of useless symbols, inaccessible symbols, empty rules, and unit rules), the existence of a Chomsky Normal Form for context-free grammars and the Pumping Lemma for context-free languages. The result is an important set of libraries covering the main results of context-free language theory, with more than 500 lemmas and theorems fully proved and checked. As it turns out, this is a comprehensive formalization of the classical context-free language theory in the Coq proof assistant and includes the formalization of the Pumping Lemma for context-free languages. The perspectives for the further development of this work are diverse and can be grouped in three different areas: inclusion of new devices and results, code extraction, and general enhancements of its libraries. (shrink)

This volume brings together a group of logic-minded philosophers and philosophically oriented logicians to address a diversity of topics on the structural analysis of non-classical logics. It mainly focuses on the construction of different types of models for various non-classical logics of current interest, including modal logics, epistemic logics, dynamic logics, and observational predicate logic. The book presents a wide range of applications of two well-known approaches in current research: structural modeling of certain philosophical issues in the framework of non-classic (...) logics, such as admissible models for modal logic, structural models for modal epistemology and for counterfactuals, and epistemological models for common knowledge and for public announcements; conceptual analysis of logical properties of, and formal semantics for, non-classical logics, such as sub-formula property, truthmaking, epistemic modality, behavioral strategies, speech acts and assertions. The structural analysis provided in this volume will appeal not only to graduate students and experts in non-classic logics, but also to readers from a wide range of disciplines, including computer science, cognitive science, linguistics, game theory and theory of action, to mention a few. (shrink)

SummaryTruth‐definitions play a crucial role in the foundations of logic and semantics. Tarsik‐type truth‐definitions are not possible to formulate in a usual first‐order language for itself, and they have been criticized because they do not account for what makes them definitions of truth. It has been suggested that truth should instead be characterized by reference to the «language‐games» of verification and falsification. The author's game‐theoretical semantics here explained for formal first‐order languages, can be thought of as a realization of (...) this idea. More technically speaking, GTS can also be thought of as a systematization of the well‐known aepsilon‐delta, definitions in the foundations of analysis. In GTS, truth is not defined by reference to winning a play of a game, but as the existence of a winning strategy in the game for the verifier. In a first‐order language, the game‐theoretical truth‐condition of a sentence S can accordingly be expressed by an explicit second‐order sentence asserting the existence of the Skolem function of S.The semantical games of GTS must be distinguished not only from the «games» of formal proof but also from the «games» in volved in our ordinary activities of verification and falsification. The latter have been modelled as games of inquiry by the author, and they are essentially epistemic games where the meaning of truth is taken for granted and where the aim of the game is to come to know certain truths. To assimilate them to the semantical games constitutive of truth is a form of Meno's paradox. (shrink)

In this paper by using a model-theoretic approach, we prove Craig interpolation property for Formal Propositional Logic, FPL, Basic propositional logic, BPL and the uniform left-interpolation property for FPL. We also show that there are countably infinite extensions of FPL with the uniform interpolation property.

We present here some modifications of tense logic based on intensionally treated game-theoretic concepts. They are intended for construction of formal models with description of intensional acts. Formal characteristic of intensional acts – subject, modus and contents; general scheme – MODUS, where x1, . . . , xm – names of subjects and A1, . . . , An – propositional description. For example: “x1 persuaded x2 that A1 is better than A2”. For the examination of formal structures, making (...) use of time logic, we should notice that an intensional act is an event identical in time with other non-intensional acts. (shrink)

Contemporary logicians have expanded upon the old notions of psychologism in logic and proposed new, weakened versions of it. Those weakened versions postulate that psychologistic logic does not have to inform about the ontology or metaphysics of reasoning. Instead, logic applied in cognitive science could serve as one of many paradigms for making empirical predictions about the observable process of human reasoning. The purpose of this article is to entertain this notion and answer the question: what properties should a (...) logical system formally representing actual human reasoning have? Based on the existing evidence from cognitive science and neuroscience we identified three potential candidates: context-sensitivity (satisfied for example by adaptive logics), content-sensitivity (satisfied by non-Fregean logics) and probabilism (satisfied for example by fuzzy logics). (shrink)

One of three distinct approaches to his famous ‘Trust’ argument, this paper written by Garfinkel in 1960, and never before published, proposed a rethinking of rules, games and linguistic classifications in interactional terms consistent with Wittgenstein’s language games. Garfinkel had been working in collaboration with Parsons since 1958 to craft an approach to culture that would replace conceptual classification with the constitutive expectancies of interaction and systems of interaction. The argument challenged the work of cultural anthropologists influenced by zoology and (...) biology, who called themselves ‘ethnoscientists’ and studied culture in terms of linguistic classification systems. Garfinkel had proposed an alternative sociological ‘ethnoscience’ of culture and language that would focus on how culture was made, on how linguistic events are achieved, and on the rules of their making. This ‘Language Games’ approach followed Wittgenstein in seeking what Garfinkel called a literal description of cultural/linguistic events: meaning by ‘literal’, a step-by-step account of the constitutive and preferred rules participants use to create a recognizable event-in-a-language. Made famous three years later in version associated with Schutz, Garfinkel’s Trust argument also appears in a 1962 text (Parsons’ Primer, published in 2019) in a version built on Parsons. (shrink)

When two people engage in a conversation, knowingly or unknowingly, they are playing a game. Players of such games have diverse objectives, or winning conditions: an applicant trying to convince her potential employer of her eligibility over that of a competitor, a prosecutor trying to convict a defendant, a politician trying to convince an electorate in a political debate, and so on. We argue that infinitary games offer a natural model for many structural characteristics of such conversations. We call (...) such games message exchange games, and we compare them to existing game theoretic frameworks used in linguistics—for example, signaling games—and show that message exchange games are needed to handle non-cooperative conversation. In this paper, we concentrate on conversational games where players’ interests are opposed. We provide a taxonomy of conversations based on their winning conditions, and we investigate some essential features of winning conditions like consistency and what we call rhetorical cooperativity. We show that these features make our games decomposition sensitive, a property we define formally in the paper. We show that this property has far-reaching implications for the existence of winning strategies and their complexity. There is a class of winning conditions for which message exchange games are equivalent to Banach- Mazur games, which have been extensively studied and enjoy nice topological results. But decomposition sensitive goals are much more the norm and much more interesting linguistically and philosophically. (shrink)

We propose a new dynamic hybrid logic to reason about social networks and their dynamics building on the work of “Logic in the Community” by Seligman, Liu and Girard. Our framework distinguishes between the purely private sphere of agents, namely their mental states, and the public sphere of their observable behavior, i.e., what they seem to believe. We then show how such a distinction allows our framework to model many social phenomena, by presenting the case of pluralistic ignorance as an (...) example and discussing some of its dynamic properties. (shrink)

The descriptive complexity of a problem is the complexity of describing the problem in some logical formalism. One of the few techniques for proving separation results in descriptive complexity is to make use of games on graphs played between two players, called the spoiler and the duplicator. There are two types of these games, which differ in the order in which the spoiler and duplicator make various moves. In one of these games, the rules seem to be tilted towards (...) favoring the duplicator. These seemingly more favorable rules make it easier to prove separation results, since separation results are proven by showing that the duplicator has a winning strategy. In this paper, the relationship between these games is investigated. It is shown that in one sense, the two games are equivalent. Specifically, each family of graphs used in one game to prove a separation result can in principle be used in the other game to prove the same result. This answers an open question of Ajtai and the author from 1989. It is also shown that in another sense, the games are not equivalent, in that there are situations where the spoiler requires strictly more resources to win one game than the other game. This makes formal the informal statement that one game is easier for the duplicator to win. (shrink)

We can distinguish different senses in which a formal language can be said to have been provided with an interpretation. We focus on two: (i) We provide a model (or structure) and a definition of satisfaction and truth in the standard way (ii) We provide a translation into a natural language. We argue that the sentences of a formal language interpreted as in (i) do not have meaning. A formal language interpreted as in (i) models the way the truth of (...) a sentence would be affected by two factors: the interpretation as in (ii) of the language, and a way the world might be. Viewing in this way the relation between interpreting a formal language as in (i) and as in (ii) allows us to justify the conceptual adequacy of the standard model-theoretic definitions of the properties of logical truth and logical consequence. (shrink)

The two concepts of probability used in physics are analyzed from the formal and the material points of view. The standard theory corresponds toprob 1 (probability of the coexistence of two properties). A general logicomathematical theory ofprob 2 (probability of transition between states) is presented in axiomatic form. The underlying state algebra is neither Boolean nor Birkhoff-von Neumann but partial Boolean. In the Boolean subalgebras,prob 1 theory holds. The theory presented contains the logicomathematical foundations of quantum mechanics and, as (...) degenerate cases, the theories of stochastic games and of Markov chains. (shrink)

I defend a conception of Logic as normative for the sort of activities in which inferences super-vene, namely, reasoning and arguing. Toulmin’s criticism of formal logic will be our framework to shape the idea that in order to make sense of Logic as normative, we should con-ceive it as a discipline devoted to the layout of arguments, understood as the representations of the semantic, truth relevant, properties of the inferences that we make in arguing and reason-ing.

The article studies properties of functional dependencies between strategies of players in Nash equilibria of multiplayer strategic games. The main focus is on the properties of functional dependencies in the context of a fixed dependency graph for payoff functions. A logical system describing properties of functional dependence for any given graph is proposed and is proven to be complete.

Some students in the humanities take fright when introduced to the formal manipulations characteristic of elementary sentential & predicate logic. One way to lessen the pain of initiation is to start with word games, of which Lewis Carroll’s Doublets (section 1) is a familiar example. The paper presents some other games that successively introduce more of the..

On September 6, 2004, using the Isabelle proof assistant, I verified the following statement: (%x. pi x * ln (real x) / (real x)) ----> 1 The system thereby confirmed that the prime number theorem is a consequence of the axioms of higher-order logic together with an axiom asserting the existence of an infinite set. All told, our number theory session, including the proof of the prime number theorem and supporting libraries, constitutes 673 pages of proof scripts, or roughly 30,000 (...) lines. This count includes about 65 pages of elementary number theory that we had at the outset, developed by Larry Paulson and others; also about 50 pages devoted to a proof of the law of quadratic reciprocity and properties of Euler’s ϕ function, neither of which are used in the proof of the prime number theorem. The page count does not include the basic HOL library, or properties of the real numbers that we obtained from the HOL-Complex library. (shrink)

Formal learning theory formalizes the process of inferring a general result from examples, as in the case of inferring grammars from sentences when learning a language. In this work, we develop a general framework—the supervised learning game—to investigate the interaction between Teacher and Learner. In particular, our proposal highlights several interesting features of the agents: on the one hand, Learner may make mistakes in the learning process, and she may also ignore the potential relation between different hypotheses; on the (...) other hand, Teacher is able to correct Learner’s mistakes, eliminate potential mistakes and point out the facts ignored by Learner. To reason about strategies in this game, we develop a modal logic of supervised learning and study its properties. Broadly, this work takes a small step towards studying the interaction between graph games, logics and formal learning theory. (shrink)

We consider systems of rational agents who act and interact in pursuit of their individual and collective objectives. We study and formalise the reasoning of an agent, or of an external observer, about the expected choices of action of the other agents based on their objectives, in order to assess the reasoner’s ability, or expectation, to achieve their own objective. To formalize such reasoning we extend Pauly’s Coalition Logic with three new modal operators of conditional strategic reasoning, thus introducing the (...) Logic for Local Conditional Strategic Reasoning \. We provide formal semantics for the new conditional strategic operators in concurrent game models, introduce the matching notion of bisimulation for each of them, prove bisimulation invariance and Hennessy–Milner property for each of them, and discuss and compare briefly their expressiveness. Finally, we also propose systems of axioms for each of the basic operators of \ and for the full logic. (shrink)

In this paper, the set-theoretic approach in the logical theory of normative systems is extended using Broome’s definition of the normative code function. The syntax and semantics for first order metanormative language is defined, and metanormative language is applied in the formalization of the basic principles in Broome’s approach and in the construction of a logical typology of normative systems. Special attention is given to the types of normative systems which are not definable in terms of the (...) class='Hi'>properties of singular sets of requirements (e.g. the realization equivalence of codes, the social compatibility of codes, and the compatibility of codes issued by different normative sources). Examples are given of the application of the typology in the interpretation of philosophical texts. Von Wright’s hypothesis on the connection of logical properties of normative systems, conceived set-theoretically, with standard deontic logic is proved by introducing the translation function between the metanormative language and the restricted language of standard deontic logic. The translation reveals that von Wright’s hypothesis must be appended. The problems of narrow and wide scope readings of the deontic conditionals and of the meaning of iterated deontic operators are addressed using the distinction between relative and absolute normative codes. The theorem on the existence of a realization equivalent absolute code for any relative code is proved. (shrink)

Three variants of Kurt Gödel's ontological argument, proposed by Dana Scott, C. Anthony Anderson and Melvin Fitting, are encoded and rigorously assessed on the computer. In contrast to Scott's version of Gödel's argument the two variants contributed by Anderson and Fitting avoid modal collapse. Although they appear quite different on a cursory reading they are in fact closely related. This has been revealed in the computer-supported formal analysis presented in this article. Key to our formal analysis is the utilization of (...) suitably adapted notions of ultrafilters, and a careful distinction between extensions and intensions of positive properties. (shrink)