From logic design to logic programming: Theorem proving techniques and P-functions

Theorem Proving Techniques and P-functions for Logic Design and Logic Programming

It is shown that theorem proving methods can lead to program synthesis and algorithm implementation by using pairs of logic laws: a deductive law for proving the theorem and a constructive law for synthesizing the program or algorithm. The construction of program schemata in an algorithmic programming environment and logic programming in a declarative programming environment appear as two parti...

Logic Programming and Theorem Proving

This paper presents a new system, called the A-System, performing abductive reasoning within theframework of Abductive Logic Programming. It isbased on a hybrid computational model that imple-ments the abductive search in terms of two tightlycoupled processes: a reduction process of the high-level logical representation to a lower-level con-straint store and a lo...

On Merging Theorem Proving and Logic Programming Paradigms (Poster Abstract)

(Poster Abstract) In this poster session, we present the current results of ongoing projects on deduction, disjunctive logic programming, and information management systems, at the University of Koblenz, Germany. The central idea behind these projects is to apply techniques and concepts developed for theorem proving in disjunctive logic programming (thereby achieving a tight integration between...

Theorem Proving and Programming with Dynamic First Order Logic

Theorem Proving for Classical Logic with Partial Functions by Reduction to Geometric Kleene Logic

Partial functions are abundant in mathematics and program specifications. Unfortunately, their importance has been mostly ignored in automated theorem proving. In this paper, we develop a theorem proving strategy for Partial Classical Logic (PCL). Proof search takes place in Kleene Logic. We show that PCL theories can be translated into sets of formulas in Kleene logic. For proof search in Klee...