In resolution proof procedures refinements based on A-orderings of literals have a long tradition and are well investigated. In tableau proof proceduressuch refinements were only recently introduced by the authors of the present paper. In this paper we prove the following results: we give a completeness proof of A-ordered ground clause tableaux which is a lot easier to follow than the previous ...

Motivated primarily by medical terminology applications, the prominent DL SHIQ has already been extended to a DL with complex role inclusion axioms of the form R ◦ S v̇ R or S ◦ R v̇ R, called RIQ, and the SHIQ tableau algorithm has been extended to handle such inclusions. This paper further extends RIQ and its tableau algorithm with important expressive means that are frequently requested in ont...

An informal tutorial is presented for program synthesis, with an emphasis on deductive methods. According to this approach, to construct a program meeting a given specification, we prove the existence of an object meeting the specified conditions. The proof is restricted to be sufficiently constructive, in the sense that, in establishing the existence of the desired output, the proof is forced ...

" Hyper tableau " is a sound and complete calculus for first-order clausal logic. The present paper introduces an improvement which removes the major weakness of the calculus, which is the need to (at least partially) blindly guess ground-instantiations for certain clauses. This guessing is now replaced by a unification-driven technique. The calculus is presented in detail, which includes a com...

Image interpretation is a dynamic research domain involving not only the detection of objects in a scene but also the semantic description considering context information in the whole scene. Image interpretation problem can be formalized as an abductive reasoning problem, i.e. an inference to the best explanation using a background knowledge. In this work, we present a framework using a tableau...

For applications of first-order automated theorem provers in a wider verification context it is essential to provide a means of presenting and checking automatically found proofs. In this paper we present a new method of transforming disconnection tableau proofs found by the prover system DCTP into a series of resolution inferences representing a resolution refutation of the proof problem.

This paper is concerned with providing a context based logic (language + semantics) for the representation of agents’s beliefs. While different approaches that make use of a single theory have been proposed in order to model agent’s beliefs, such as modal logics, these often suffer from problems, as lack of modularity, logical omniscence, and dissimilarity with implementations. A partial soluti...