Logicality as Necessary Instantiation

On Negation As Instantiation

Given a logic program P and a goal G, we introduce a notion which states when an SLD-tree for P fGg instantiates a set of variables V with respect to another one, W. We call this notion weak instantiation, as it is a generalisation of the instantiation property introduced by Di Pierro, Martelli and Palamidessi. A negation rule based on instanti-ation, the so-called Negation As Instantiation rul...

Negation as Instantiation

We propose a new negation rule for logic programming which derives existentially closed negative literals, and we de ne a version of completion for which this rule is sound and complete. The rule is called \Negation As Instantiation" (NAI). According to it, a negated atom succeeds whenever all the branches of the SLD-tree for the atom either fail or instantiate the atom. The set of the atoms wh...

Logicality and Invariance

This paper deals with the problem of giving a principled characterization of the class of logical constants. According to the so-called Tarski-Sher thesis, an operation is logical iff it is invariant under permutation. In the model-theoretic tradition, this criterion has been widely accepted as giving a necessary condition for an operation to be logical. But it has been also widely criticized o...

Logicality of Conditional Rewrite Systems

A conditional term rewriting system is called logical if it has the same logical strength as the underlying conditional equational system. In this paper we summarize known logicality results and we present new sufficient conditions for logicality of the important class of oriented conditional term rewriting systems.

The Logicality of Abduction, Deduction and Induction