Frank Veltman

Provability logics for relative interpretability

In this paper the system IL for relative interpretability described in Visser (1988) is studied.1 In IL formulae A ⊳ B (read: A interprets B) are added to the provability logic L. The intended interpretation of a formula A ⊳ B in an (arithmetical) theory T is: T + B is relatively interpretable in T + A. The system has been shown to be sound with respect to such arithmetical interpretations (Svejdar 1983, Montagna 1984, Visser 1986, 1988P).

An Update on ’’Might‘‘

This paper is on the update semantics for “might” of Veltman (1996). Threeconsequence relations are introduced and studied in an abstract setting.Next we present sequent-style systems for each of the consequence relations.We show the logics to be complete and decidable. The paper ends with asyntactic cut elimination result.

Making the right exceptions

This paper is about the logical properties of sentences of the form Ss are normally P, and starts from the idea that any logical theory for such sentences should meet the following simple requirement: If the only available information about some object x is that x has property S, it must be valid to infer by default that x has all the properties P that objects with property S normally have. We investigate how this requirement can be met by theories developed within the framework of circumscription, and specify a constraint - the exemption principle - that must be satisfied to do so. This principle determines in cases of conflicting default rules which objects are exempted from which rules, and, as such, is the main source for the capricious logical behavior of the sentences we are interested in.To facilitate comparison (and implementation) we supply an algorithm for inheritance networks and prove that arguments that can be expressed in both frameworks are valid on the circumscriptive account if and only if the inheritance algorithm has a positive outcome.