The non-classical, nonmonotonic inference relation associated with the answer set semantics for logic programs gives rise to a relationship of strong equivalence between logical programs that can be veriied in 3-valued GG odel logic, G3, the strongest non-classical intermediate propositional logic (Lifschitz, Pearce and Valverde, 2001). In this paper we… (More)
This article ~s a report on research m progress into the structure of fimte diagrams of mtuinomst~c proposmonal logic with the aid of automated reasoning systems for larger calculanons. A/ragment of a proposmonal logic is the set of formulae built up from a fimte number of proposinonal variables by means of a number of connectives of the logic, among which… (More)
We extend Angluin's (1980) theorem to characterize identiiability of indexed families of r.e. languages, as opposed to indexed families of recursive languages. We also prove some variants characterizing conservativity a n d t wo other similar restrictions, paralleling Zeug-mann, Lange, and Kapur's (1992, 1995) results for indexed families of recursive… (More)
We investigate fragments of intuitionistic propositional logic containing implication but not disjunction. These fragments are finite, but their size grows superexponentially with the number of generators. Exact models are used to characterize the fragments.
In this article we prove the Jankov Theorem for extensions of IPC () and the Jankov Theorem for KC () in a uniform frame-theoretic way in the setting of n-universal models for IPC. In frame-theoretic terms, the first Jankov Theorem states that for each finite rooted frame there is a formula ψ with the property that any counter-model for ψ needs this… (More)
abstract. In this article we study interpolation properties for the minimal system of interpretability logic IL. We prove that arrow interpolation holds for IL and that turnstile interpolation and interpolation for the £-modality easily follow from this result. Furthermore , these properties are extended to the system ILP. Failure of arrow interpolation for… (More)
—Inspired by a similar use in provability logic, formulas p B q and p B q are introduced in the existing logical framework for discussing beliefs to express that the strength of belief in p is greater than (or equal to) that in q. This explicit mention of the comparison in the logical language aids in defining several other concepts in a uniform way, viz.… (More)
In this paper we study IL(PRA), the interpretability logic of PRA. As PRA is neither an essentially reflexive theory nor finitely axiomatizable, the two known arithmetical completeness results do not apply to PRA: IL(PRA) is not ILM or ILP. IL(PRA) does of course contain all the principles known to be part of IL(All), the interpretability logic of the… (More)