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)

"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.

Edna Ullmann-Margalit provides an original account of the emergence of norms. Her main thesis is that certain types of norms are possible solutions to problems posed by certain types of social interaction situations. She presents illuminating discussions of Prisoners' Dilemma, co-ordination, and inequality situations.

_ 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.

Counterfactuals is David Lewis' forceful presentation of and sustained argument for a particular view about propositions which express contrary to fact conditionals, including his famous defense of realism about possible worlds and his theory of laws of nature.

Using probability functions defined over a simple language as models of states of belief, my goal in this article has been to analyse contractions and revisions of beliefs. My first strategy was to formulate postulates for these processes. Close parallels between the postulates for contractions and the postulates for revisions have been established - the results in Section 5 show that contractions and revisions are interchangeable. As a second strategy, some suggestions for more or less explicit constructive definitions of the (...) revision process (and indirectly also of the contraction process) were then presented. However, the results in Section 6 are less conclusive than in the earlier ones. This problem area still awaits further development. (shrink)

A feature of David Lewis's account of conventions in his book "Convention" which has received admiring notices from philosophers is his use of the mathematical theory of games. In this paper I point out a number of serious flaws in Lewis's use of game theory. Lewis's basic claim is that conventions cover 'coordination problems'. I show that game-Theoretical analysis tends to establish that coordination problems in Lewis's sense need not underlie conventions.

The question whether and in what way languages and language use involve convention is addressed, With special reference to David Lewis's account of convention in general. Data are presented which show that Lewis has not captured the sense of 'convention' involved when we speak of adopting a linguistic convention. He has, In effect, attempted an account of social conventions. An alternative account of social convention and an account of linguistic convention are sketched.

In the days when the Great Central and the Midland ran competitive services from Leicester to London, I agreed to meet your train when you came up from Leicester. “It arrives at 12.5”, you said in your letter. But you neglected to mention which station, and only on the morning of your journey did each of us realize that this matter had been left open. You intended to travel from Leicester Central, it being more convenient for you than London Road, (...) and you supposed that I would be able to infer your intention by consulting Bradshaw, and noting a 12.5 arrival from Leicester at Marylebone. (shrink)

Analyzes the nature of international disagreements and conflict resolution in terms of game theory and non-zero-sum games.