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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.

- Dick de Jongh
- 2009

The extension property up to n and T n –projectivity. We refine a well–known theorem of Ghilardi published in [1] which establishes the equivalence between the extension property and projectivity. The definitions of these two notions are as follows: • A formula ϕ has the extension property if we can add a node below an arbitrary collection of rooted Kripke… (More)

In this article we prove the Jankov Theorem for extensions of IPC ([6]) and the Jankov Theorem for KC ([7]) 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)