This anthology is a thorough introduction to classic literature for those who have not yet experienced these literary masterworks. For those who have known and loved these works in the past, this is an invitation to reunite with old friends in a fresh new format. From Shakespeare's finesse to Oscar Wilde's wit, this unique collection brings together works as diverse and influential as The Pilgrim's Progress and Othello. As an anthology that invites readers to immerse themselves in the masterpieces of (...) the literary giants, it is must-have addition to any library. (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)

This Is A New Release Of The Original 1897 Edition.

This introduction to modern work in analytic philosophy uses the example of the proper name to give a clear explanation of the logical theories of Gottlob Frege, and explain the application of his ideas to ordinary language. McCulloch then shows how meaning is rooted in the philosophy of mind and the question of intentionality, and looks at the ways in which thought can be "about" individual material objects.

Epistemic agents may have different powers of observation and reasoning, and we show how this diversity fits into dynamic update logics.RésuméLes agents épistémiques peuvent avoir différents pouvoirs d’observation et de raisonnement, et nous montrons comment cette diversité prend place en logique dynamique de mise à jour.

Some fictionalist approaches to the notion of scientific model are based on the concept of game of make-believe developed by Kendall Walton, without proposing a similar interpretation of it. The distinction between authorized and unauthorized games can be one of the sources of those divergences. In relation to the distinction made by Walton, the de dicto and de re modalities of the fiction-operator reflect different epistemological engagements concerning objects which satisfy properties. This paper aims at following up on the (...) proposals formulated by Roman Frigg and Adam Toon by using some modal logic concepts, notably by defining the identities of properties in modal contexts in terms of world-lines. Applying a model to a target-system consists in transposing fictional truths into actual situations, through an extrapolation that goes beyond the games of make-believe. (shrink)

numbers as in the following example ♦1,1♦1,2 2,3 5,4p We denote the set of formulas of this modal language by M L(k). For each modality type i, there will be an accessibility relation Ri. That is, an k-ary modal structure for the modal propositional language L will have the form..

_An in-depth look at the philosophical issues behind HBO's _Game of Thrones_ television series and the books that inspired it_ George R.R. Martin's _New York Times_ bestselling epic fantasy book series, A Song of Ice and Fire, and the HBO television show adapted from it, have earned critical acclaim and inspired fanatic devotion. This book delves into the many philosophical questions that arise in this complex, character-driven series, including: Is it right for a "good" king to usurp the throne of (...) a "bad" one and murder his family? How far should you go to protect your family and its secrets? In a fantasy universe with medieval mores and ethics, can female characters reflect modern feminist ideals? Timed for the premiere of the second season of the HBO _Game of Thrones_ series Gives new perspectives on the characters, storylines, and themes of _Game of Thrones_ Draws on great philosophers from ancient Greece to modern America to explore intriguing topics such as the strange creatures of Westeros, the incestuous relationship of Jaime and Cersei Lannister, and what the kings of Westeros can show us about virtue and honor as they play their game of thrones Essential reading for fans, _Game of Thrones and Philosophy_ will enrich your experience of your favorite medieval fantasy series. (shrink)

Since the first chapter of this book presents an intro duction to the present state of game-theoretical semantics (GTS), there is no point in giving a briefer survey here. Instead, it may be helpful to indicate what this volume attempts to do. The first chapter gives a short intro duction to GTS and a survey of what is has accomplished. Chapter 2 puts the enterprise of GTS into new philo sophical perspective by relating its basic ideas to Kant's phi losophy (...) of mathematics, space, and time. Chapters 3-6 are samples of GTS's accomplishments in understanding different kinds of semantical phenomena, mostly in natural languages. Beyond presenting results, some of these chapters also have other aims. Chapter 3 relates GTS to an interesting line of logical and foundational studies - the so-called functional interpretations - while chapter 4 leads to certain important methodological theses. Chapter 7 marks an application of GTS in a more philo sophical direction by criticizing the Frege-Russell thesis that words like "is" are multiply ambiguous. This leads in turn to a criticism of recent logical languages (logical notation), which since Frege have been based on the ambi guity thesis, and also to certain methodological sug gestions. In chapter 8, GTS is shown to have important implications for our understanding of Aristotle's doctrine of categories, while chapter 9 continues my earlier criticism of Chomsky's generative approach to linguistic theorizing. (shrink)

I argue that the medieval form of dialectical disputation known as obligationes can be viewed as a logical game of consistency maintenance. The game has two participants, Opponent and Respondent. Opponent puts forward a proposition P; Respondent must concede, deny or doubt, on the basis of inferential relations between P and previously accepted or denied propositions, or, in case there is none, on the basis of the common set of beliefs. Respondent loses the game if he concedes a contradictory set (...) of propositions. Opponent loses the game if Respondent is able to maintain consistency during the stipulated period of time. The obligational rules are here formalised by means of familiar notational devices, and the application of some game-theoretical concepts, such as (winning) strategy, moves, motivation, allows for an analysis of some crucial properties of the game. In particular, the primacy of inferential (syntactic) relations over semantic aspects and the dynamic character of obligations are outlined. (shrink)

Graph games are interactive scenarios with a wide range of applications. This position paper discusses old and new graph games in tandem with matching logics and identifies general questions behind this match. Throughout, we pursue two strands: logic as a way of analyzing existing graph games, and logic as an inspiration for designing new graph games. Our aim is modest: we propose a perspective that complements existing game-theoretic and computational ones, we raise questions, make (...) observations, and suggest research directions—technical results are left to future work. But frankly, our main aim with this survey paper is to show that graph games are concrete, fun, easy to grasp, and yet challenging to study. (shrink)

Truth, consistency and elementary equivalence can all be characterised in terms of games, namely the so-called evaluation game, the model-existence game, and the Ehrenfeucht–Fraisse game. We point out the great affinity of these games to each other and call this phenomenon the strategic balance in logic. In particular, we give explicit translations of strategies from one game to another.

For the past 20 years or so the literature on noncooperative games has been centered on the search for an equilibrium concept that expresses the notion of rational behavior in interactive situations. A basic tenet in this literature is that if a “rational solution” exists, it must be a Nash equilibrium. The consensus view, however, is that not all Nash equilibria can be accepted as rational solutions. Consider, for example, the game of Figure 1.

I. Levi has advocated a decision-theoretic account of belief revision. We argue that the game-theoretic framework of Interrogative Inquiry Games, proposed by J. Hintikka, can extend and clarify this account. We show that some strategic use of the game rules generate Expansions, Contractions and Revisions, and we give representation results. We then extend the framework to represent explicitly sources of answers, and apply it to discuss the Recovery Postulate. We conclude with some remarks about the potential extensions of interrogative (...) games, with respect to some issues in the theory of belief change. (shrink)

We study partiality in propositional logics containing formulas with either undefined or over-defined truth-values. Undefined values are created by adding a four-place connective W termed transjunction to complete models which, together with the usual Boolean connectives is shown to be functionally complete for all partial functions. Transjunction is seen to be motivated from a game-theoretic perspective, emerging from a two-stage extensive form semantic game of imperfect information between two players. This game-theoretic approach yields an interpretation where partiality is generated as (...) a property of non-determinacy of games. Over-defined values are produced by adding a weak, contradictory negation or, alternatively, by relaxing the assumption that games are strictly competitive. In general, particular forms of extensive imperfect information games give rise to a generalised propositional logic where various forms of informational dependencies and independencies of connectives can be studied. (shrink)

This paper does not deal with the applications of game theory for which this theory was first developed, that is, for modelling economic systems and rational decision making. But I do not want to consider games as abstract mathematical structures, either. I want to concentrate on what it is that makes a game actually playable. This playability means both the possibility of finding and formulating the strategy that a player uses and the feasibility of actually applying the strategy in (...) question in making one’s moves. (shrink)

Over the past decades, logicians interested in rational agency and intelligent interaction studied major components of these phenomena, such as knowledge, belief, and preference. In recent years, standard ‘static’ logics describing information states of agents have been generalized to dynamic logics describing actions and events that produce information, revise beliefs, or change preferences, as explicit parts of the logical system. Van Ditmarsch, van der Hoek & Kooi 2007, Baltag, van Ditmarsch & Moss 2008, van Benthem, to appear A, are up-to-date (...) accounts of this dynamic trend (the present paper follows Chapter 9 of the latter book). But in reality, concrete rational agency contains all these dynamic processes entangled. A concrete setting for this entanglement are games – and this paper is a survey of their interfaces with logic, both static and dynamic. Games are intriguing also since their analysis brings together two major streams, or tribal communities: ‘hard’ mathematical logics of computation, and ‘soft’ philosophical logics of propositional attitudes. Of course, this hard/soft distinction is spurious, and there is no natural border line between the two sources: it is their congenial mixture that makes current theories of agency so lively. (shrink)

This paper develops an account of Wittgenstein’s method of language-games as a method of logic that exhibits important continuities with Russell’s and the early Wittgenstein’s conceptions of logic and logical analysis as the method of philosophy. On the proposed interpretation, the method of language-games is a method for isolating and modeling aspects of the uses of linguistic expressions embedded in human activities that enables one to make perspicuous complex uses of expressions by gradually building up the (...) complexity of clarificatory models. Wittgenstein’s introduction of the language-game method constitutes an attempt to overcome certain limitations of calculus-based logical methods, and to respond in this way to problems with Russell’s and his own early philosophy of logic. The method is nevertheless compatible with the employment of calculus-based methods in logic and philosophy, and makes no exclusive claim to being the correct method. (shrink)

I LOGIC IN PHILOSOPHY— PHILOSOPHY OF LOGIC i. On the relation of logic to philosophy I n this book, the consequences of certain logical insights for ...

Several results about the game of cops and robbers on infinite graphs are analyzed from the perspective of computability theory. Computable robber-win graphs are constructed with the property that no computable robber strategy is a winning strategy, and such that for an arbitrary computable ordinal \, any winning strategy has complexity at least \}\). Symmetrically, computable cop-win graphs are constructed with the property that no computable cop strategy is a winning strategy. Locally finite infinite trees and graphs are explored. The (...) Turing computability of a binary relation used to classify cop-win graphs is studied, and the computational difficulty of determining the winner for locally finite computable graphs is discussed. (shrink)

In recent work, semantic games of independence-friendly logic were studied in strategic form in terms of Nash equilibria. The class of strategic games of independence-friendly logic is contained in the class of win-loss, zero-sum two-player games. In this note we draw on the theory of linear programming to develop tools to analyze the value of such games. We give two applications of these tools to independence-friendly logic under the so-called equilibrium semantics.

This collection of papers in epistemic logic is oriented towards applications to game theory and individual decision theory. Most of these papers were presented at the inaugural conference of the LOFT (Logic for the Theory and Games and Decisions) conference series, which took place in 1994 in Marseille. Among the notions dealt with are those of common knowledge and common belief, infinite hierarchies of beliefs and belief spaces, logical omniscience, positive and negative introspection, backward induction and rationalizable (...) equilibria in game theory. (shrink)

In [Dutilh Novaes, Medieval-obligations as logical Games of Consistency maintenance, synthese, (2004)], I proposed a reconstruction of Walter Burley’s theory of obligationes, based on the idea that Burley’s theory of obligationes could be seen as a logical game of consistency maintenance. In the present paper, I intend to test the game hypothesis on another important theory of obligationes, namely Roger Swyneshed’s theory. In his treatise on obligationes [edited by P.V. Spade, cf. Spade History and philosophy of Logic 3(1982) (...) 1-32], Swyneshed introduced significant modifications to the general framework of obligationes. To compare the two theories, I apply the same formal apparatus used in the previous paper. It will become patent that Swyneshed’s theory is considerably different from Burley’s, among other reasons because the dynamic aspects that play a major role in the latter are simply not present in the former. My conclusion is that Swyneshed’s version of obligationes is not directed towards consistency maintenance, but rather towards inference recognition, and that it is, from a game-theoretical perspective, less interesting a theory than Burley’s. (shrink)

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

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)

This book offers a comprehensive account of logic that addresses fundamental issues concerning the nature and foundations of the discipline. The authors claim that these foundations can not only be established without the need for strong metaphysical assumptions, but also without hypostasizing logical forms as specific entities. They present a systematic argument that the primary subject matter of logic is our linguistic interaction rather than our private reasoning and it is thus misleading to see logic as revealing (...) "the laws of thought". In this sense, fundamental logical laws are implicit to our "language games" and are thus more similar to social norms than to the laws of nature. Peregrin and Svoboda also show that logical theories, despite the fact that they rely on rules implicit to our actual linguistic practice, firm up these rules and make them explicit. By carefully scrutinizing the project of logical analysis, the authors demonstrate that logical rules can be best seen as products of the so called reflective equilibrium. They suggest that we can profit from viewing languages as "inferential landscapes" and logicians as "geographers" who map them and try to pave safe routes through them. This book is an essential resource for scholars and researchers engaged with the foundations of logical theories and the philosophy of language. (shrink)

The first-order logical theory Th $({\mathbb{N}},x + 1,F(x))$ is proved to be complete for the class ATIME-ALT $(2^{O(n)},O(n))$ when $F(x) = 2^{x}$ , and the same result holds for $F(x) = c^{x}, x^{c} (c \in {\mathbb{N}}, c \ge 2)$ , and F(x) = tower of x powers of two. The difficult part is the upper bound, which is obtained by using a bounded Ehrenfeucht–Fraïssé game.

Twenty-five years after the end of the Cold War, a new Cold War is being waged in our societies. During the Cold War a theoretical model of man was developed by economists and the military, an egotistical being interested only in his own benefit and in duping his opponents to achieve his ends: a modern homo oeconomicus. After his career in the Cold War ended, he was not scrapped but adapted to the needs of the twenty-first century. He became the (...) ringmaster of a new era of information capitalism. He sought to read, control and influence thoughts; to predict, price and eliminate risks. Today stock-market trading is guided by him. He uses computer algorithms and Big Data to build up detailed pictures of our preferences and then suggest and sell goods to us. The model has become a self-fulfilling prophecy. We are no longer the masters of our own fate. The Game of Life runs without us. Schirrmacher traces the progress of this extreme rationalization of social life from the Cold War games of the 1950s Rand Corporation to the stock-market trading techniques that brought about the financial crash of 2008, showing how these developments were interwoven with the rise of game theory, rational choice theory and neoliberal economics. The state and politics increasingly submitted themselves to the logic of computerized game theory and an economistic view of the world, evading real decision-making in the process. In this brave new world individuals, alone in front of their computers, may think they are constructing a reality of their own choosing, but in fact they are being manipulated all along by others who are setting the rules of the game. This international bestseller by one of Germanys most distinguished journalists is a powerful indictment of a way of thinking that has become pervasive and threatens to undermine not only parliaments and constitutions but also the sovereignty of the individual to be the person he or she wants to be. (shrink)

We consider an infinite two-person game. The second player has a winning perfect information strategy; we show that this player has a winning strategy which depends on substantially less information. The game studied here is a variation on a game of Gale.

The ancient problems of bankruptcy, contested garment, and rights arbitration have generated many studies, debates, and controversy. The objective of this paper is to show that the Shapley value from game theory, measuring the power of each player in a game, may be consistently applied for getting the general one-step solution of all these three problems viewed as -person games. The decision making is based on the same tool, namely the game theory logic based on the use of (...) the Shapley value, but the specific games involved are slightly different in each problem. The kind of claims of the players, the relationship between the given claims and the given resources available, and the particular way of calculating the generalized characteristic function of the game determine the specific type of game which has to be solved in each of the three ancient problems mentioned. The iterative use of the Shapley value may also justify the well-known Aumann-Maschler step-by-step procedure for solving the bankruptcy problem. (shrink)

We continue the work initiated in Herzig and Lorini (J Logic Lang Inform, in press) whose aim is to provide a minimalistic logical framework combining the expressiveness of dynamic logic in which actions are first-class citizens in the object language, with the expressiveness of logics of agency such as STIT and logics of group capabilities such as CL and ATL. We present a logic called ( Deterministic Dynamic logic of Agency ) which supports reasoning about actions (...) and joint actions of agents and coalitions, and agentive and coalitional capabilities. In it is supposed that, once all agents have selected a joint action, the effect of this joint action is deterministic. In order to assess we prove that it embeds Coalition Logic. We then extend with modal operators for agents’ preferences, and show that the resulting logic is sufficiently expressive to capture the game-theoretic concepts of best response and Nash equilibrium. (shrink)

IntroductionA quick glance at the opening paragraphs in many of the classic logic textbooks reveals a common view: Logical methods highlight the reasoning patterns of a single agent engaged in some form of mathematical thinking.A sampling from my bookshelf: Shoenfield’s Mathematical Logic: “Logic is the study of reasoning; and mathematical logic is the study of the type of reasoning done by mathematicians”; Enderton’s A Mathematical Introduction of Logic: “Symbolic logic is a mathematical model of (...) deductive thought”; and Chiswell and Hodges Mathematical Logic: “In this course we shall study some ways of proving statements.” However, this traditional view of the “subject matter” of logic is expanding. There is a growing literature using phrases such as “rational interaction” or “information flow” to describe its subject matter while still employing traditional logical methods. The clearest example of this can be found in the work of Johan van Benthem and others on l .. (shrink)

Recent literary methods have opened new possibilities in reading and understanding the logic of narratives. The Greimassian approach offers such a possibility. Though Greimas’ approach is by now accepted as part of the canon of narratology, some of its components have not yet received due attention. This is the case with his ‘veridictory square’, a diagram that applies especially to texts where oppositions such as truth-falsehood, hero-villain and subject-anti-subject are prominent themes. This article aims to demonstrate that these kinds (...) of narratives, such as Susanna, do not concern themselves with objective truth but persuasion about truth, that is, veridiction. Truth telling in those stories corresponds to manipulation, exercising a particular cognitive doing or causing to appear as true. In other words, such a manipulation of truth aims at causing people to believe. Using Greimas’ veridictory square built on opposing modalities of being and seeming, the contrast between reality and appearance, this article provides insight into the games of truth in Susanna and thus offers a new inspiring way of reading these kinds of stories. (shrink)

We discuss a simple logic to describe one of our favourite games from childhood, hide and seek, and show how a simple addition of an equality constant to describe the winning condition of the seeker makes our logic undecidable. There are certain decidable fragments of first-order logic which behave in a similar fashion and we add a new modal variant to that class of logics. We also discuss the relative expressive power of the proposed logic (...) in comparison to the standard modal counterparts. (shrink)

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.

This volume is a collects papers originally presented at the 7th Conference on Logic and the Foundations of Game and Decision Theory (LOFT), held at the University of Liverpool in July 2006. LOFT is a key venue for presenting research at the intersection of logic, economics, and computer science, and this collection gives a lively and wide-ranging view of an exciting and rapidly growing area.

I propose a modal logic that enables to reason about self-regarding and otherregarding motivations in strategic games. This logic integrates the concepts of joint action, belief, individual and group payoff. The first part of the article is focused on self-regarding agents. A self-regarding agent decides to perform a certain action only if he believes that this action maximizes his own personal benefit. The second part of the article explores different kinds of other-regarding motivations such as fairness and (...) reciprocity. Differently from self-regarding agents, other-regarding agents also consider the benefits of their choices for the group. Moreover, their decisions can be affected by their beliefs about other agents' willingness to act for the well-being of the group. The analysis also considers team-directed reasoning, i.e. the mode of reasoning that people use when they take themselves to be acting as members of a group or a team. (shrink)