We develop a denotational, fully abstract semantics for constraint logic programming (clp) with respect to successful and failed observables. The denotational approach turns out very useful for the deenition of new operators on the language as the counterpart of some abstract operations on the denotational domain. In particular, by deening our domain as a cylindric Heyting algebra, we can explo...

Modern explanatory ILP methods like Progol, Residue procedure, CF-induction, HAIL and Imparo use the principle of Inverse Entailment (IE). It is based on the fact that the negation of a hypothesis is derived from a prior background theory and the negation of examples. IE-based methods commonly compute a hypothesis in two steps: by first constructing an intermediate theory and next by generalizi...

The mediaeval logic of Aristotelian privation, represented by Ockham’sexposition of All A is non-P as All S is of a type T that is naturally P and no S isP, is critically evaluated as an account of privative negation. It is argued thatthere are two senses of privative negation: (1) an intensifier (as in subhuman),the inverse of Neoplatonic hypernegation (superhuman), which is st...

This paper presents a framework to understand negation in positive terms. Specifically, we extract positive meaning from negation when the negation cue syntactically modifies a noun or adjective. Our approach is grounded on generating potential positive interpretations automatically, and then scoring them. Experimental results show that interpretations scored high can be reliably identified.

We introduce intuitionistic and classical substructural logics with structural rules mingle and connective strong negation, and investigate the cut-elimination property and the relevance principle for these logics. The relevance principle does not hold for substructural logics with mingle and usual negation, but holds for those with mingle and strong negation.