Partial implication semantics in the context of a background theory has been introduced to formalize partial goal satisfaction in the context of beliefs. In this paper, we introduce strong partial implication prohibiting redundancies and weak partial implication allowing side effects, we study their semantic as well as complexity properties, and we apply the three notions of partial implication...

This investigation, in Bishop’s constructive mathematics in sense of well-known books [2], [3], [6] and Romano’s papers [9]-[15], is continuation of forthcoming Crvenkovic, Mitrovic and Romano’s paper [4], and the Romano’s paper [16]. Bishop’s constructive mathematics is developed on Constructive logic (or Intuitionistic logic ([19])) logic without the Law of Excluded Middle P ∨¬¬P . Let us not...

In a recent work by Demri and Deters (CSL-LICS 2014), first-order separation logic restricted to two variables and separating implication was shown undecidable, where it was shown that even with only two variables, if the use of negations is unrestricted, then they can be nested with separating implication in a complex way to get the undecidability result. In this paper, we revisit the decidabi...

The aim of this paper is to provide a semantics for general logic programs (with negation by default) extended with explicit negation, subsuming well founded semantics 22]. The Well Founded semantics for extended logic programs (WFSX) is expressible by a default theory semantics we have devised 11]. This relationship improves the cross{fertilization between logic programs and default theories, ...

Abstract. Bi-intuitionistic logic is the extension of intuitionistic logic with a connective dual to implication. Bi-intuitionistic logic was introduced by Rauszer as a Hilbert calculus with algebraic and Kripke semantics. But her subsequent “cut-free” sequent calculus for BiInt has recently been shown by Uustalu to fail cut-elimination. We present a new cut-free sequent calculus for BiInt, and...

We consider the problem of verification condition generation for Abadi and Leino’s program logic (AL) for objects. We provide an algorithm which to a given judgement J in AL computes a formula φ in first-order fixpoint logic such that φ is equivalent to the existence of a proof of J in AL. Moreover, we show that if J is sufficiently annotated, e.g., with loop invariants, then φ will be purely f...