In Minimal Rationality, Christopher Cherniak boldly challenges the myth of Man the the Rational Animal and the central role that the "perfectly rational...

A semantics is presented for belief revision in the face of common announcements to a group of agents that have beliefs about each other’s beliefs. The semantics is based on the idea that possible worlds can be viewed as having an internal-structure, representing the belief independent features of the world, and the respective belief states of the agents in a modular fashion. Modularity guarantees that changing one aspect of the world (a belief independent feature or a belief state) has no (...) effect on any other aspect of the world. This allows us to employ an AGM-style selection function to represent revision. The semantics is given a complete axiomatisation (identical to the axiomatisation found by Gerbrandy and Groeneveld for a semantics based on non-wellfounded set theory) for the special case of expansion. (shrink)

A semantics is presented for belief-revision in the face of common announcements to a group of agents that have beliefs about each other's beliefs. The semantics is based on the idea that possible worlds can be viewed as having an internal structure, representing the belief independent features of the world, and the respective belief states of the agents in a modular fashion. Modularity guarantees that changing one aspect of the world (a belief independent feature or a belief state) has no (...) effect on any other aspect of the world. This allows us to employ an AGM-style selection function to represent revision. The semantics is given a complete axiomatisation (identical to the axiomatisation found by Gerbrandy and Groeneveld for a semantics based on non-wellfounded set theory) for the special case of expansion. (shrink)

What happens to our conception of mind and rational agency when we take seriously future-directed intentions and plans and their roles as inputs into further practical reasoning? The author's initial efforts in responding to this question resulted in a series of papers that he wrote during the early 1980s. In this book, Bratman develops further some of the main themes of these essays and also explores a variety of related ideas and issues. He develops a planning theory of intention. Intentions (...) are treated as elements of partial plans of action. These plans play basic roles in practical reasoning, roles that support the organization of our activities over time and socially. Bratman explores the impact of this approach on a wide range of issues, including the relation between intention and intentional action, and the distinction between intended and expected effects of what one intends. (shrink)

This paper supersedes an ealier version, entitled "A Non-Standard Semantics for Inexact Knowledge with Introspection", which appeared in the Proceedings of "Rationality and Knowledge". The definition of token semantics, in particular, has been modified, both for the single- and the multi-agent case.

This modern, advanced textbook reviews modal logic, a field which caught the attention of computer scientists in the late 1970's.

Current dynamic-epistemic logics model different types of information change in multi-agent scenarios. We generalize these logics to a probabilistic setting, obtaining a calculus for multi-agent update with three natural slots: prior probability on states, occurrence probabilities in the relevant process taking place, and observation probabilities of events. To match this update mechanism, we present a complete dynamic logic of information change with a probabilistic character. The completeness proof follows a compositional methodology that applies to a much larger class of dynamic-probabilistic (...) logics as well. Finally, we discuss how our basic update rule can be parameterized for different update policies, or learning methods. (shrink)

We construct logical languages which allow one to represent a variety of possible types of changes affecting the information states of agents in a multi-agent setting. We formalize these changes by defining a notion of epistemic program. The languages are two-sorted sets that contain not only sentences but also actions or programs. This is as in dynamic logic, and indeed our languages are not significantly more complicated than dynamic logics. But the semantics is more complicated. In general, the semantics of (...) an epistemic program is what we call aprogram model. This is a Kripke model of ‘actions’,representing the agents' uncertainty about the current action in a similar way that Kripke models of ‘states’ are commonly used in epistemic logic to represent the agents' uncertainty about the current state of the system. Program models induce changes affecting agents' information, which we represent as changes of the state model, called epistemic updates. Formally, an update consists of two operations: the first is called the update map, and it takes every state model to another state model, called the updated model; the second gives, for each input state model, a transition relation between the states of that model and the states of the updated model. Each variety of epistemic actions, such as public announcements or completely private announcements to groups, gives what we call an action signature, and then each family of action signatures gives a logical language. The construction of these languages is the main topic of this paper. We also mention the systems that capture the valid sentences of our logics. But we defer to a separate paper the completeness proof. (shrink)

In update logic as studied by Baltag, Moss, Solecki and van Benthem, little attention is paid to the interpretation of an action by an agent, which is just assumed to depend on the situation. This is actually a complex issue that nevertheless complies to some logical dynamics. In this paper, we tackle this topic. We also deal with actions that change propositional facts of the situation. In parallel, we propose a formalism to accurately represent an agent's epistemic state based on (...) hyperreal numbers. In that respect, we use infinitesimals to express what would surprise the agents (and by how much) by contradicting their beliefs. We also use a subjective probability to model the notion of belief. It turns out that our probabilistic update mechanism satisfies the AGM postulates of belief revision. (shrink)

We describe a general logical framework, Justification Logic, for reasoning about epistemic justification. Justification Logic is based on classical propositional logic augmented by justification assertions t: F that read t is a justification for F. Justification Logic absorbs basic principles originating from both mainstream epistemology and the mathematical theory of proofs. It contributes to the studies of the well-known Justified True Belief vs. Knowledge problem. We state a general Correspondence Theorem showing that behind each epistemic modal logic, there is a (...) robust system of justifications. This renders a new, evidence-based foundation for epistemic logic. As a case study, we offer a resolution of the GoldmanRed Barns in Justification Logic. Furthermore, we formalize the well-known Gettier example and reveal hidden assumptions and redundancies in Gettier’s reasoning. (shrink)

In 1933 Godel introduced a calculus of provability (also known as modal logic S4) and left open the question of its exact intended semantics. In this paper we give a solution to this problem. We find the logic LP of propositions and proofs and show that Godel's provability calculus is nothing but the forgetful projection of LP. This also achieves Godel's objective of defining intuitionistic propositional logic Int via classical proofs and provides a Brouwer-Heyting-Kolmogorov style provability semantics for Int which (...) resisted formalization since the early 1930s. LP may be regarded as a unified underlying structure for intuitionistic, modal logics, typed combinatory logic and λ-calculus. (shrink)

We present a framework for verifying systems composed of heterogeneous reasoning agents, in which each agent may have differing knowledge and inferential capabilities, and where the resources each agent is prepared to commit to a goal (time, memory and communication bandwidth) are bounded. The framework allows us to investigate, for example, whether a goal can be achieved if a particular agent, perhaps possessing key information or inferential capabilities, is unable (or unwilling) to contribute more than a given portion of its (...) available computational resources or bandwidth to the problem. We present a novel temporal epistemic logic, BMCL-CTL , which allows us to describe a set of reasoning agents with bounds on time, memory and the number of messages they can exchange. The bounds on memory and communication are expressed as axioms in the logic. As an example, we show how to axiomatise a system of agents which reason using resolution and prove that the resulting logic is sound and complete. We then show how to encode a simple system of reasoning agents specified in BMCL-CTL in the description language of the Mocha model checker (Alur et al., Proceedings of the tenth international conference on computer-aided verification (CAV) , 1998), and verify that the agents can achieve a goal only if they are prepared to commit certain time, memory and communication resources. (shrink)

This paper extends earlier work by its authors on formal aspects of the processes of contracting a theory to eliminate a proposition and revising a theory to introduce a proposition. In the course of the earlier work, Gardenfors developed general postulates of a more or less equational nature for such processes, whilst Alchourron and Makinson studied the particular case of contraction functions that are maximal, in the sense of yielding a maximal subset of the theory (or alternatively, of one of (...) its axiomatic bases), that fails to imply the proposition being eliminated. In the present paper, the authors study a broader class, including contraction functions that may be less than maximal. Specifically, they investigate "partial meet contraction functions", which are defined to yield the intersection of some nonempty family of maximal subsets of the theory that fail to imply the proposition being eliminated. Basic properties of these functions are established: it is shown in particular that they satisfy the Gardenfors postulates, and moreover that they are sufficiently general to provide a representation theorem for those postulates. Some special classes of partial meet contraction functions, notably those that are "relational" and "transitively relational", are studied in detail, and their connections with certain "supplementary postulates" of Gardenfors investigated, with a further representation theorem established. (shrink)

This book develops a view of logic as a theory of information-driven agency and intelligent interaction between many agents - with conversation, argumentation and games as guiding examples. It provides one uniform account of dynamic logics for acts of inference, observation, questions and communication, that can handle both update of knowledge and revision of beliefs. It then extends the dynamic style of analysis to include changing preferences and goals, temporal processes, group action and strategic interaction in games. Throughout, the book (...) develops a mathematical theory unifying all these systems, and positioning them at the interface of logic, philosophy, computer science and game theory. A series of further chapters explores repercussions of the 'dynamic stance' for these areas, as well as cognitive science. (shrink)

Karl Raimund Poppers (1902-1994) Hauptwerk, die Logik der Forschung (1934), gilt als Grundlagenwerk des kritischen Rationalismus. Der kritische Rationalismus zeigt, warum unser Wissen fehlbar ist und versteht den Erkenntnisfortschritt als Resultat von Hypothesenbildung und -widerlegung. Der Sammelband orientiert sich an der Gliederung der Logik der Forschung. Seine Beiträge kommentieren die jeweiligen Themen nach aktueller Forschungslage.

Knowledge and its Limits presents a systematic new conception of knowledge as a kind of mental stage sensitive to the knower's environment. It makes a major contribution to the debate between externalist and internalist philosophies of mind, and breaks radically with the epistemological tradition of analyzing knowledge in terms of true belief. The theory casts new light on such philosophical problems as scepticism, evidence, probability and assertion, realism and anti-realism, and the limits of what can be known. The arguments are (...) illustrated by rigorous models based on epistemic logic and probability theory. The result is a new way of doing epistemology and a notable contribution to the philosophy of mind. (shrink)

Challenging, with several powerful arguments, some of our deepest beliefs about rationality, morality, and personal identity, Parfit claims that we have a false view about our own nature. It is often rational to act against our own best interersts, he argues, and most of us have moral views that are self-defeating. We often act wrongly, although we know there will be no one with serious grounds for complaint, and when we consider future generations it is very hard to avoid conclusions (...) that most of us will find very disturbing. (shrink)

Hunting Causes and Using Them argues that causation is not one thing, as commonly assumed, but many. There is a huge variety of causal relations, each with different characterizing features, different methods for discovery and different uses to which it can be put. In this collection of new and previously published essays, Nancy Cartwright provides a critical survey of philosophical and economic literature on causality, with a special focus on the currently fashionable Bayes-nets and invariance methods - and it exposes (...) a huge gap in that literature. Almost every account treats either exclusively how to hunt causes or how to use them. But where is the bridge between? It's no good knowing how to warrant a causal claim if we don't know what we can do with that claim once we have it. This book will interest philosophers, economists and social scientists. (shrink)

"The best book available for non-mathematicians." — Contemporary Psychology. Superb nontechnical introduction to game theory and related disciplines, primarily as applied to the social sciences. Clear, comprehensive coverage of utility theory, 2-person zero-sum games, 2-person non-zero-sum games, n-person games, individual and group decision-making, much more. Appendixes. Bibliography. Graphs and figures.

Dynamic Epistemic Logic is the logic of knowledge change. This book provides various logics to support such formal specifications, including proof systems. Concrete examples and epistemic puzzles enliven the exposition. The book also offers exercises with answers. It is suitable for graduate courses in logic. Many examples, exercises, and thorough completeness proofs and expressivity results are included. A companion web page offers slides for lecturers and exams for further practice.

This is the classic work upon which modern-day game theory is based. What began as a modest proposal that a mathematician and an economist write a short paper together blossomed, when Princeton University Press published Theory of Games and Economic Behavior. In it, John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific inquiry (...) it yielded--game theory--has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences. (shrink)

This is an expository paper in which the basic ideas of a family of Justification Logics are presented. Justification Logics evolved from a logic called LP, introduced by Sergei Artemov [1, 3], which formed the central part of a project to provide an arithmetic semantics for propositional intuitionistic logic. The project was successful, but there was a considerable bonus: LP came to be understood as a logic of knowledge with explicit justifications and, as such, was capable of addressing in a (...) natural way long-standing problems of logical omniscience. Since then, LP has become one member of a family of related logics, all logics of knowledge with explicit knowledge terms. In this paper the original problem of intuitionistic foundations is discussed only briefly. We concentrate entirely on issues of reasoning about knowledge. (shrink)

Most of our knowledge is inexact, and known by us to be so. An example of such known inexactness will be described in some detail. The description seems to entail a contradiction. However, the paradoxical reasoning rests on an assumption. It will be suggested that the description is correct and this assumption false. Its failure will be explained by means of a picture of inexact knowledge in which the notion of a margin for error is central. This picture suggests diagnoses (...) of other paradoxical arguments: Surprise Examinations, backwards inductions about Iterated Prisoner's Dilemma, and the Heap. (shrink)

We look at two fundamental logical processes, often intertwined in planning and problem solving: inference and update. Inference is an internal process with which we uncover what is implicit in the information we already have. Update, on the other hand, is produced by external communication, usually in the form of announcements and in general in the form of observations, giving us information that might not have been available (even implicitly) before. Both processes have received attention from the logic community, usually (...) separately. In this work, we develop a logical language that allows us to describe them together. We present syntax, semantics and a complete axiom system; we discuss similarities and differences with other approaches and mention how the work can be extended. (shrink)

The aim of this paper is twofold: (i) to introduce the framework of update semantics and to explain what kind of semantic phenomena may successfully be analysed in it: (ii) to give a detailed analysis of one such phenomenon: default reasoning.

In an information state where various agents have both factual knowledge and knowledge about each other, announcements can be made that change the state of information. Such informative announcements can have the curious property that they become false because they are announced. The most typical example of that is 'fact p is true and you don't know that', after which you know that p, which entails the negation of the announcement formula. The announcement of such a formula in a given (...) information state is called an unsuccessful update. A successful formula is a formula that always becomes common knowledge after being announced. Analysis of information systems and 'philosophical puzzles' reveals a growing number of dynamic phenomena that can be described or explained by unsuccessful updates. This increases our understanding of such philosophical problems. We also investigate the syntactic characterization of the successful formulas. (shrink)

Suppose we have a stack of cards that is divided over some players. For certain distributions of cards it is possible to communicate your hand of cards to another player by public announcements, without yet another player learning any of your cards. A solution to this problem consists of some sequence of announcements and is called an exchange. It is called a direct exchange if it consists of (the minimum of) two announcements only. The announcements in an exchange have a (...) special form: they are safe communications, an interesting new form of update. Certain unsafe communications turn out to be unsuccessful updates. A communication is a public announcement that is known to be true. Each communication may be about a set of alternative card deals only, and even about a set of alternatives to the communicating player's own hand only. We list the direct exchanges for a deal of seven cards where the two players holding three cards communicate their hands to each other. Our work may be applicable to the design of cryptographic protocols. (shrink)

Rational agents are important objects of study in several research communities, including economics, philosophy, cognitive science, and most recently computer science and artificial intelligence. Crudely, a rational agent is an entity that is capable of acting on its environment, and which chooses to act in such a way as to further its own best interests. There has recently been much interest in the use of mathematical logic for developing formal theories of such agents. Such theories view agents as practical reasoning (...) systems, deciding moment by moment which action to perform next, given the beliefs they have about the world and their desires with respect to how they would like the world to be. In this article, we survey the state of the art in developing logical theories of rational agency. Following a discussion on the dimensions along which such theories can vary, we briefly survey the logical tools available in order to construct such theories. We then review and critically assess three of the best known theories of rational agency: Cohen and Levesque's intention logic, Rao and Georgeff's BDI logics, and the KARO framework of Meyer et al. We then discuss the various roles that such logics can play in helping us to engineer rational agents, and conclude with a discussion of open problems. (shrink)

In ‘belief revision’ a theory is revised with a formula φ resulting in a revised theory . Typically, is in , one has to give up belief in by a process of retraction, and φ is in . We propose to model belief revision in a dynamic epistemic logic. In this setting, we typically have an information state (pointed Kripke model) for the theory wherein the agent believes the negation of the revision formula, i.e., wherein is true. The revision with (...) φ is a program *φ that transforms this information state into a new information state. The transformation is described by a dynamic modal operator [*φ], that is interpreted as a binary relation [ [*φ] ] between information states. The next information state is computed from the current information state and the belief revision formula. If the revision is successful, the agent believes φ in the resulting state, i.e., Bφ is then true. To make this work, as information states we propose ‘doxastic epistemic models’ that represent both knowledge and degrees of belief. These are multi-modal and multi-agent Kripke models. They are constructed from preference relations for agents, and they satisfy various characterizable multi-agent frame properties. Iterated, revocable, and higher-order belief revision are all quite natural in this setting. We present, for an example, five different ways of such dynamic belief revision. One can also see that as a non-deterministic epistemic action with two alternatives, where one is preferred over the other, and there is a natural generalization to general epistemic actions with preferences. (shrink)

A variety of logical frameworks have been developed to study rational agents interacting over time. This paper takes a closer look at one particular interface, between two systems that both address the dynamics of knowledge and information flow. The first is Epistemic Temporal Logic (ETL) which uses linear or branching time models with added epistemic structure induced by agents’ different capabilities for observing events. The second framework is Dynamic Epistemic Logic (DEL) that describes interactive processes in terms of epistemic event (...) models which may occur inside modalities of the language. This paper systematically and rigorously relates the DEL framework with the ETL framework. The precise relationship between DEL and ETL is explored via a new representation theorem characterizing the largest class of ETL models corresponding to DEL protocols in terms of notions of Perfect Recall , No Miracles , and Bisimulation Invariance . We then focus on new issues of completeness . One contribution is an axiomatization for the dynamic logic of public announcements constrained by protocols, which has been an open problem for some years, as it does not fit the usual ‘reduction axiom’ format of DEL. Finally, we provide a number of examples that show how DEL suggests an interesting fine-structure inside ETL. (shrink)

Contemporary logic is confined to a few paradigmatic attitudes such as belief, knowledge, desire and intention. My purpose is to present a general modeltheoretical semantics of propositional attitudes of any cognitive or volitive mode. In my view, one can recursively define the set of all psychological modes of attitudes. As Descartes anticipated, the two primitive modes are those of belief and desire. Complex modes are obtained by adding to primitive modes special cognitive and volitive ways or special propositional content or (...) preparatory conditions. According to standard logic of attitudes , human agents are either perfectly rational or totally irrational. I will proceed to a finer analysis of propositional attitudes that accounts for our imperfect but minimal rationality. For that purpose I will use a non standard predicative logic according to which propositions with the same truth conditions can have different cognitive values and I will explicate subjective in addition to objective possibilities. Next I will enumerate valid laws of my general logic of propositional attitudes. At the end I will state principles according to which minimally rational agents dynamically revise attitudes of any mode. (shrink)

To describe simultaneous knowledge updates for different subgroups we propose anepistemic language with dynamic operators for actions. The language is interpreted onequivalence states (S5 states). The actions are interpreted as state transformers. Two crucial action constructors are learning and local choice. Learning isthe dynamic equivalent of common knowledge. Local choice aids in constraining theinterpretation of an action to a functional interpretation (state transformer).Bisimilarity is preserved under execution of actions. The language is applied todescribe various actions in card games.

We show how belief revision can be treated systematically in the format of dynamicepistemic logic, when operators of conditional belief are added. The core engine consists of definable update rules for changing plausibility relations between worlds, which have been proposed independently in the dynamic-epistemic literature on preference change. Our analysis yields two new types of modal result. First, we obtain complete logics for concrete mechanisms of belief revision, based on compositional reduction axioms. Next, we show how various abstract postulates for (...) belief revision can be analyzed by standard modal frame correspondences for model-changing operations. (shrink)

Statements not only update our current knowledge, but also have other dynamic effects. In particular, suggestions or commands ?upgrade' our preferences by changing the current order among worlds. We present a complete logic of knowledge update plus preference upgrade that works with dynamic-epistemic-style reduction axioms. This system can model changing obligations, conflicting commands, or ?regret'. We then show how to derive reduction axioms from arbitrary definable relation changes. This style of analysis also has a product update version with preferences between (...) actions, as well as worlds. Some illustrations are presented involving defaults and obligations. We conclude that our dynamic framework is viable, while admitting a further extension to more numerical ?utility update'. (shrink)