80 research outputs found
First order theories for nonmonotone inductive definitions: recursively inaccessible and Mahlo
In this paper first order theories for nonmonotone inductive definitions are introduced, and a proof-theoretic analysis for such theories based on combined operator forms à la Richter with recursively inaccessible and Mahlo closure ordinals is give
Some observations about generalized quantifiers in logics of imperfect information
We analyse the two definitions of generalized quantifiers for logics of dependence and independence that have been proposed by F. Engstrom. comparing them with a more general, higher order definition of team quantifier. We show that Engstrom's definitions (and other quantifiers from the literature) can be identified, by means of appropriate lifts, with special classes of team quantifiers. We point out that the new team quantifiers express a quantitative and a qualitative component, while Engstrom's quantifiers only range over the latter. We further argue that Engstrom's definitions are just embeddings of the first-order generalized quantifiers into team semantics. and fail to capture an adequate notion of team-theoretical generalized quantifier, save for the special cases in which the quantifiers are applied to flat formulas. We also raise several doubts concerning the meaningfulness of the monotone/nonmonotone distinction in this context. In the appendix we develop some proof theory for Engstrom's quantifiers.Peer reviewe
FO(FD): Extending classical logic with rule-based fixpoint definitions
We introduce fixpoint definitions, a rule-based reformulation of fixpoint
constructs. The logic FO(FD), an extension of classical logic with fixpoint
definitions, is defined. We illustrate the relation between FO(FD) and FO(ID),
which is developed as an integration of two knowledge representation paradigms.
The satisfiability problem for FO(FD) is investigated by first reducing FO(FD)
to difference logic and then using solvers for difference logic. These
reductions are evaluated in the computation of models for FO(FD) theories
representing fairness conditions and we provide potential applications of
FO(FD).Comment: Presented at ICLP 2010. 16 pages, 1 figur
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