We present a new execution strategy for constraint logic programs called Failure Tabled CLP. Similarly to Tabled CLP our strategy records certain derivations in order to prune further derivations. However, our method only learns from failed derivations. This allows us to compute interpolants rather than constraint projection for generation of reuse conditions. As a result, our technique can be ...

We present a procedure for computing the sceptical “ideal semantics” for argumentation in assumption-based frameworks. This semantics was first proposed for logic programming in [1], extending the well-founded semantics. The proof procedure is defined by means of a form of dispute derivations, obtained by modifying the dispute derivations given in [2] for computing credulous admissible argument...

The Curry-Howard correspondence connects natural deduction derivation with the lambdacalculus. Predicates are types, derivations are terms. This supports reasoning from assumptions to conclusions, but we may want to reason backwards; from the desired conclusion towards the assumptions. At intermediate stages we may have a partial derivation, with holes. This is natural in informal practice but ...

We present a new set of reductions for derivations in natural deduction that can extract witnesses from closed derivations of simply existential formulas in Heyting Arithmetic (HA) plus the Excluded Middle Law restricted to simply existential formulas (EM1), a system motivated by its interest in proof mining. The reduction we have for classical logic are quite different from all existing ones. ...

In this paper we argue that sequent proofs systems are a better deductive apparatus for introducing proofs to students than are natural deduction systems. Natural deduction derivations of superintuitionistic theorems (theorems of classical logic that are not intuitionistically valid) require indirect and often obtuse constructions. Constructing derivations in sequent systems is uniform, driven ...

The paper introduces a semantics for logic programs based on rst order hereditary Harrop formulas which are expressed in terms of intuitionistic derivations. The derivations are constructed by means of an intuitionistic proof procedure that constitutes the resolution mechanism of the language. The semantics of a program is a goal independent denotation which can be equivalently speciied by a de...

In (Porat et al., 1982, Inform. and Control 55, 108-116) the notion of fair derivations in context-free grammars was introduced and studied. The main result there is a characterization of fairly terminating grammars as non-uaria6le-doubling. In this paper we show that the same characterization is valid under canonical deriuations in which the next variable to be expanded is deterministically ch...

derivations, equational logic and interpolation Gerard R. Renardel de Lavalette Department of Mathematics and Computing Science University of Groningen, the Netherlands Abstract. We define abstract derivations for equational logic and use them to prove the interpolation property. We define abstract derivations for equational logic and use them to prove the interpolation property.

In this paper we show how the notion of tree dimension can be used in the verification of constrained Horn clauses (CHCs). The dimension of a tree is a numerical measure of its branching complexity and the concept here applies to Horn clause derivation trees. Derivation trees of dimension zero correspond to derivations using linear CHCs, while trees of higher dimension arise from derivations us...

The basic algebraic structures within the categories of derivations determined by rewriting systems are presented. The similarity congruence relation in categories of derivations is given in three versions. The syntax category is formed by taking derivations modulo similarity. This category is a free strict monoidal category, a simple form of a 2-category. The syntax category is central to the ...