The mathematical theory of communication.

"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.

Recently, natural language pragmatics started to make use of decision-, game-, and information theoretical tools to determine the usefulness of questions and assertions in a quantitative way. In the first part of this paper several of these notions are related with each other. It is shown that under particular natural assumptions the utility of questions and answers reduces to their informativity, and that the ordering relation induced by utility sometimes even reduces to the logical relation of entailment. The second part (...) of the paper shows how different proposals (using either protocols or likelihood functions) to measure the relevance/utility of non-partitional questions come down to the same thing. (shrink)

In this paper I will discuss why (un) marked expressionstypically get an (un)marked interpretation: Horn''sdivision of pragmatic labor. It is argued that it is aconventional fact that we use language this way.This convention will be explained in terms ofthe equilibria of signalling games introduced byLewis (1969), but now in an evolutionary setting. Iwill also relate this signalling game analysis withParikh''s (1991, 2000, 2001) game-theoretical analysis ofsuccessful communication, which in turn is compared withBlutner''s: 2000) bi-directional optimality theory.

Why do we ask questions? Because we want tohave some information. But why this particular kind ofinformation? Because only information of this particularkind is helpful to resolve the decision problemthat the agent faces. In this paper I argue thatquestions are asked because their answers help toresolve the questioner's decision problem, and that thisassumption helps us to interpret interrogativesentences. Interrogative sentences are claimed to have asemantically underspecified meaning and thisunderspecification is resolved by means of the decisionproblem.

Dynamic update of information states is a new paradigm in logicalsemantics. But such updates are also a traditional hallmark ofprobabilistic reasoning. This note brings the two perspectives togetherin an update mechanism for probabilities which modifies state spaces.

A utility-based approach to the understanding of vague predicates (VPs) is proposed. It is argued that assignment of truth values to propositions containing VPs entails unjustifiable assumptions of consensus; two models of VP semantics are criticized on this basis: (1) the super-truth theory of Kit Fine (1975), which requires an unlikely consensus on base points; (2) the fuzzy logic of Lotfi Zadeh (1975), on fuzzy truth values of sentences. Pragmatism is held to provide a key: successful behavior justifies a person's (...) knowledge of the content of a VP. Instead of attempting to determine a consensus underlying successful communication, the utility of individual communications is held to rest on sufficient approximation of meanings between people. 3 Figures, 17 References. Adapted from the source document. (shrink)

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)

_ Convention_ was immediately recognized as a major contribution to the subject and its significance has remained undiminished since its first publication in 1969. Lewis analyzes social conventions as regularities in the resolution of recurring coordination problems-situations characterized by interdependent decision processes in which common interests are at stake. Conventions are contrasted with other kinds of regularity, and conventions governing systems of communication are given special attention.

In this paper I combine the dynamic epistemic logic ofGerbrandy (1999) with the probabilistic logic of Fagin and Halpern (1994). The resultis a new probabilistic dynamic epistemic logic, a logic for reasoning aboutprobability, information, and information change that takes higher orderinformation into account. Probabilistic epistemic models are defined, and away to build them for applications is given. Semantics and a proof systemis presented and a number of examples are discussed, including the MontyHall Dilemma.

In this paper we introduce Dynamic Epistemic Logic, which is alogic for reasoning about information change in a multi-agent system. Theinformation structures we use are based on non-well-founded sets, and canbe conceived as bisimulation classes of Kripke models. On these structures,we define a notion of information change that is inspired by UpdateSemantics (Veltman, 1996). We give a sound and complete axiomatization ofthe resulting logic, and we discuss applications to the puzzle of the dirtychildren, and to knowledge programs.

Classic analysis of the subject and the development of personal probability; one of the greatest controversies in modern statistcal thought.