Game-theoretic inductive definability

Truth and Inductive Definability

The purpose of this note is to give an exposition of Kripke’s theory of truth [4] within the context of the theory of induction on abstract structures. The results are not presented in full generality: That is not needed for the applications made here. For that, see Moschovakis [6], Kechris and Moschovakis, [2], and McGee [5, ch. 5]. Useful papers here, besides Kripke’s original, include Feferm...

Inductive Definability and the Situation Calculus

We explore the situation calculus within the framework of inductive deenability. A consequence of this view of the situation calculus is to establish direct connections with diierent variants of the-First we show that the induction principle on situations Reiter, 1993] is implied by an inductive deenition of the set of situations. Then we consider the frame problem from the point of view of ind...

Inductive Definability with Counting on Finite Structures

Infinitary Logic and Inductive Definability over Finite Structures

The extensions of first-order logic with a least fixed point operators (FO + LFP) and with a partial fixed point operator (FO + PFP) are known to capture the complexity classes P and PSPACE respectively in the presence of an ordering relation over finite structures. Recently, Abiteboul and Vianu [AV91b] investigated the relation of these two logics in the absence of an ordering, using a mchine ...

Prequential probability: game-theoretic = measure theoretic

This article continues study of the prequential framework for evaluating a probability forecaster. Testing the hypothesis that the sequence of forecasts issued by the forecaster is in agreement with the observed outcomes can be done using prequential notions of probability. It turns out that there are two natural notions of probability in the prequential framework: game-theoretic, whose idea go...