Reasoning about equilibria in normal form games involves the study of players’ incentives to deviate unilaterally from any profile. In the case of large anonymous games, the pattern of reasoning is different. Payoffs are determined by strategy distributions rather than strategy profiles. In such a game each player would strategise based on expectations of what fraction of the population makes some choice, rather than respond to individual choices by other players. A player may not even know how many players there (...) are in the game. Logicising such strategisation involves many challenges as the set of players is potentially unbounded. This suggests a logic of quantification over player variables and modalities for player deviation, but such a logic is easily seen to be undecidable. Instead, we propose a propositional modal logic using player types as names and implicit quantification over players. With modalities for player deviation and transitive closure, the logic can be used to specify game equilibrium and interesting patterns of reasoning in large games. We show that the logic is decidable and present a complete axiomatisation of the valid formulas. (shrink)

In large anonymous games, payoffs are determined by strategy distributions rather than strategy profiles. If half the players choose a strategy a, all of them get a certain payoff, whereas if only one-third of the players choose that strategy, the players choosing may get a different payoff. Strategizing in such a game by a player involves reasoning about not who does what but what fraction of the population makes the same choice as that player.We present a simple modal logic to (...) reason about such strategization in large games. Since actual numbers are irrelevant, a player need not even know how many others are in the game, thus leading to the consideration of games with unboundedly many players. The logic we consider is the propositional modal fragment of a first order modal logic. We show that it has a bounded agent property, giving us a decision procedure for satisfiability. We also present a complete axiomatization of the valid formulas. The logic admits a natural model checking algorithm and bisimulation characterization. The logic with quantification over players is more appropriate, but is undecidable. (shrink)

We study term modal logics, where modalities can be indexed by variables that can be quantified over. We suggest that these logics are appropriate for reasoning about systems of unboundedly many reasoners and define a notion of bisimulation which preserves propositional fragment of term modal logics. Also we show that the propositional fragment is already undecidable but that its monodic fragment is decidable, and expressive enough to include interesting assertions.

When we reason about strategic games, implicitly we need to reason about arbitrary strategy profiles and how players can improve from each profile. This structure is exponential in the number of players. Hence it is natural to look for subclasses of succinct games for which we can reason directly by interpreting formulas on the (succinct) game description rather than on the associated improvement structure. Priority separable games are one of such subclasses: payoffs are specified for pairwise interactions, and from these, (...) payoffs are computed for strategy profiles. We show that equilibria in such games can be described in Monadic Least Fixed Point Logic (MLFP). We then extend the description to games over arbitrarily many players, but using the monadic least fixed point extension of existential second order logic. (shrink)

We suggest that developing automata theoretic foundations is relevant for knowledge theory, so that we study not only what is known by agents, but also the mechanisms by which such knowledge is arrived at. We define a class of epistemic automata, in which agents’ local states are annotated with abstract knowledge assertions about others. These are finite state agents who communicate synchronously with each other and information exchange is ‘perfect’. We show that the class of recognizable languages has good closure (...) properties, leading to a Kleene-type theorem using what we call regular knowledge expressions. These automata model distributed causal knowledge in the following way: each agent in the system has a partial knowledge of the temporal evolution of the system, and every time agents synchronize, they update each other’s knowledge, resulting in a more up-to-date view of the system state. Hence we show that these automata can be used to solve the satisfiability problem for a natural epistemic temporal logic for local properties. Finally, we characterize the class of languages recognized by epistemic automata as the regular consistent languages studied in concurrency theory. (shrink)

Preface of Festschrift on the occasion of Professor Rohit Parikh's 60th birthday.

We study repeated normal form games where the number of players is large. We argue that it is interesting to look at such games as being divided into subgames, each of which we call a neighbourhood. The structure of such a game is given by a graph G whose nodes are players and edges denote visibility. The neighbourhoods are maximal cliques in G. The game proceeds in rounds where in each round the players of every clique X of G play (...) a strategic form game among each other. A player at a node v strategises based on what she can observe, i.e., the strategies and the outcomes in the previous round of the players at vertices adjacent to v. Based on this, the player may switch strategies in the same neighbourhood, or migrate to another neighbourhood.We are interested in addressing questions regarding the eventual stability of such games. We incrementally impose constraints on the ‘types’ of the players. First, we look at players who are unconstrained in their strategising abilities, in that, players who may use unbounded memory. We then consider the case of memoryless players. We show that in both these cases the eventual stability of the game can be characterised in terms of potentials. We then introduce a simple modal logic in which the types of the players can be specified. We show that when the players play according to these specified types, it can be effectively decided whether the game stabilises. Finally, we look at the important heuristic of imitation. Simple imitative strategies can be specified in the logic introduced by us. We show that in a population of optimisers and imitators, we can decide how ‘worse-off’ the imitators are by playing imitative strategies rather than optimal ones. (shrink)

The Asian Logic Conference (ALC) is a major international event in mathematical logic. It features the latest scientific developments in the fields of mathematical logic and its applications, logic in computer science, and philosophical logic. The ALC series also aims to promote mathematical logic in the Asia-Pacific region and to bring logicians together both from within Asia and elsewhere for an exchange of information and ideas. This combined proceedings volume represents works presented or arising from the 14th and 15th ALCs.

Розкрито сутність поняття «рейтинг». Доведено значущість рейтингової оцінки для суб’єктів фінансового ринку, зокрема для страхових компаній, потенційних страхувальників, інвесторів та кредиторів.

We investigate the semantics of messages, and argue that the meaning ofa message is naturally and usefully given in terms of how it affects theknowledge of the agents involved in the communication. We note thatthis semantics depends on the protocol used by the agents, and thus not only the message itself, but also the protocol appears as a parameter in the meaning. Understanding this dependence allows us to give formal explanations of a wide variety of notions including language dependence, implicature, (...) and the amount of information in a message. (shrink)

"Williams's masterful translation satisfies (at last!) a long-standing need. There are lots of good translations of Augustine's great work, but until now we have been forced to choose between those that strive to replicate in English something of the majesty and beauty of Augustine's Latin style and those that opt instead to convey the careful precision of his philosophical terminology and argumentation. Finally, Williams has succeeded in capturing both sides of Augustine's mind in a richly evocative, impeccably reliable, elegantly readable (...) presentation of one of the most impressive achievements in Western thought--Augustine's Confessions." --Scott MacDonald, Professor of Philosophy and Norma K. Regan Professor in Christian Studies, Cornell University. (shrink)

This book discusses major milestones in Rohit Jivanlal Parikh’s scholarly work. Highlighting the transition in Parikh’s interest from formal languages to natural languages, and how he approached Wittgenstein’s philosophy of language, it traces the academic trajectory of a brilliant scholar whose work opened up various new avenues in research. This volume is part of Springer’s book series Outstanding Contributions to Logic, and honours Rohit Parikh and his works in many ways. Parikh is a leader in the realm of ideas, offering (...) concepts and definitions that enrich the field and lead to new research directions. Parikh has contributed to a variety of areas in logic, computer science and game theory. In mathematical logic his contributions have been in recursive function theory, proof theory and non-standard analysis; in computer science, in the areas of modal, temporal and dynamic logics of programs and semantics of programs, as well as logics of knowledge; in artificial intelligence in the area of belief revision; and in game theory in the formal analysis of social procedures, with a strong undercurrent of philosophy running through all his work.This is not a collection of articles limited to one theme, or even directly connected to specific works by Parikh, but instead all papers are inspired and influenced by Parikh in some way, adding structures to and enriching “Parikh-land”. The book presents a brochure-like overview of Parikh-land before providing an “introductory video” on the sights and sounds that you experience when reading the book. (shrink)

This book offers a critical introduction to the work of American philosopher D. G. Leahy (1937-2014). Leahy's fundamental thinking can be characterized as an absolute creativity in which all creating is 'live' -- a happening occurring now that manifests a supersaturated polyontological actuality that is essentially created by the logic that characterizes it. Leahy leaves behind the categorial presuppositions of modern thought, eclipsing both Cartesian and Hegelian subjectivities and introducing instead an essentially new form of thinking founded in a nondual (...) logic of creation. The new thinking delineates the absolute unicity of existence as a creative interactivity beyond all traditional dichotomies (such as one vs. many, unity vs. plurality, identity vs. change): a fully "digitized" actuality that is nothing but newness, which inherently implies nothing but change. Through this new form of thinking, change itself is revealed to be the very essence of reality and mind. Any reader looking for a quantum leap beyond the thrall of modern and postmodern fixations is invited to hear and apprehend this new thinking that refuses to be conditioned by paradigms, categories, species, genera, walls, bridges, boundaries, or abstractions: an essentially free thinking that embodies creative novelty itself. (shrink)

R.I.G Hughes offers the first detailed and accessible analysis of the Hilbert-space models used in quantum theory and explains why they are so successful.

In this first paperback edition, a new introduction by Tom Burke establishes the ongoing importance of Sleeper's analysis of the integrity of Dewey's work and ...

This book is not a study of Plato's philosophy, but a contribution to the literary interpretation of the dialogues, through analysis of their formal structure, ...

Linking the process of rational decision making to emotions, an award-winning scientist who has done extensive research with brain-damaged patients notes the dependence of thought processes on feelings and the body's survival-oriented regulators. 50,000 first printing.

Political liberals ask citizens not to appeal to certain considerations, including religious and philosophical convictions, in political deliberation. We argue that political liberals must include a demanding requirement of intellectual modesty in their ideal of citizenship in order to motivate this deliberative restraint. The requirement calls on each citizen to believe that the best reasoners disagree about the considerations that she is barred from appealing to. Along the way, we clarify how requirements of intellectual modesty relate to moral reasons for (...) deliberative restraint. And we argue against attempts to weaken our requirement of intellectual modesty by emphasizing those moral reasons. (shrink)

Many philosophers believe that there is a causal condition on perception, and that this condition is a conceptual truth about perception. A highly influential argument for this claim is based on intuitive responses to Gricean style thought experiments. Do the folk share the intuitions of philosophers? Roberts et al. (2016) presented participants with two kinds of cases: Blocker cases (similar to Grice’s case involving a mirror and a pillar) and Non-Blocker cases (similar to Grice’s case involving a clock and brain (...) stimulation). They found that a substantial minority agreed that seeing occurs in the Non-Blocker cases, and that in the Blocker cases significantly less agreed that seeing occurs. They thus hypothesized that folk intuitions better align with a no blocker condition than with a causal condition. This paper continues this line of enquiry with two new experiments. The paper investigates the generality and robustness of Roberts et al.’s findings by expanding the sense modalities tested from only vision to audition and olfaction as well. The paper also uses Gricean style thought experiments as a case study for investigating the “reflection defense” against the negative project in experimental philosophy. Our results replicate and extend Roberts et al.’s study and support their hypothesis that folk intuitions better align with a no blocker condition. They also provide an empirical reason to doubt the reflection defense. (shrink)

The Hellenistic philosophers and schools of philosophy are emerging from the shadow of Plato and Aristotle and are increasingly studied for their intrinsic philosophical value. They are not only interesting in their own right, but also form the intellectual background of the late Roman Republic. This study gives a comprehensive and readable account of the principal doctrines of the Stoics, Epicureans and various sceptical traditions from the death of Alexander the Great in 323 B.C. to around 200 A.D. Discussions are (...) arranged topically in order to address underlying issues and to make clear what the different schools have in common and how they differ. At the same time the coherence of each system as a whole is emphasized. (shrink)

The renowned philosopher John Searle reveals the fundamental nature of social reality. What kinds of things are money, property, governments, nations, marriages, cocktail parties, and football games? Searle explains the key role played by language in the creation, constitution, and maintenance of social reality. We make statements about social facts that are completely objective, for example: Barack Obama is President of the United States, the piece of paper in my hand is a twenty-dollar bill, I got married in London, etc. (...) And yet these facts only exist because we think they exist. How is it possible that we can have factual objective knowledge of a reality that is created by subjective opinions? This is part of a much larger question: How can we give an account of ourselves, with our peculiar human traits DS mind, reason, freedom, society - in a world that we know independently consists of mindless, meaningless particles? How can we account for our social and mental existence in a realm of brute physical facts? In answering this question, Searle avoids postulating different realms of being, a mental and a physical, or worse yet, a mental, a physical, and a social. There is just one reality: Searle shows how the human reality fits into that one reality. Mind, language, and civilization are natural products of the basic facts of the physical world described by physics, chemistry and biology. Searle explains how language creates and maintains the elaborate structures of human social institutions. These institutions serve to create and distribute power relations that are pervasive and often invisible. These power relations motivate human actions in a way that provides the glue that holds human civilization together. Searle shows how this account illuminates human rationality, free will, political power, and human rights. Our social world is a world created and maintained by language. (shrink)

Locke is the first English philosopher to be considered in this series, and that fact of itself is worthy of attention. Philosophy, of course, like science, knows no frontiers and no national boundaries. Yet it is true to say that Locke’s contribution to philosophy is typically and peculiarly English. His moderation, his emphasis upon experience, his tolerant spirit of compromise, his dislike of mystical extravagance and of metaphysical speculation, even that elusive quality of his which people call his “common sense”, (...) are English traits. His very defects, illogicality leading to inconsistency and an awkward disorderliness of thought so abhorrent to the. (shrink)