6 papers
On completeness of Hausdorff hyperspaces
Ján Komara
The Hausdorff hyperspace of a metric space consists of all its non-empty bounded closed sets and it is equipped with the Pompeiu--Hausdorff set distance. We present a simpler novel…
Existentially Quantified Systems of Equations as an Implicit Representation of Answers in Logic Programming
Ján Komara
In this paper we present an alternative approach to formalize the theory of logic programming. In this formalization we allow existential quantified variables and equations in quer…
Conjunctive Queries, Existentially Quantified Systems of Equations and Finite Substitutions
Ján Komara
This report presents an elementary theory of unification for positive conjunctive queries. A positive conjunctive query is a formula constructed from propositional constants, equat…
Extraction of Efficient Programs in -arithmetic
Ján Komara, Paul J. Voda
Clausal Language (CL) is a declarative programming and verifying system used in our teaching of computer science. CL is an implementation of, what we call, par…
On Herbrand Skeletons
Paul J. Voda, Ján Komara
Herbrand's theorem plays an important role both in proof theory and in computer science. Given a Herbrand skeleton, which is basically a number specifying the count of disjunctions…
Efficient elimination of Skolem functions in
Ján Komara
Elimination of a single Skolem function in pure logic increases the length of proofs only linearly. The result is shown for derivations with cuts that are free for the Skolem funct…