Formální logické systémy založené na neklauzulární rezoluci

PaedDr. Hashim HABIBALLA, Ph.D.

Doctoral thesis

Non-clausal Resolution based Formal Logical Systems

Abstract:

The thesis presents refutational resolution theorem proving system for both the classical and many-valued logics based on the general (non-clausal) resolution rule. There is also presented a unification algorithm handling existentiality without the need of skolemization. This formalism integrates properties especially suitable for description logic and for fuzzy predicate logic. The problem of automated reasoning concerning fuzzy logic requires more complex methods in contrast to classical logic. Presented formalism overcomes the key unsolvable obstacle - clausal normal form generation (in fuzzy logic) - by introduction of generally applicable inference rule (working with general formulas not only clauses). Additionally we present several inference strategies for efficient theorem proving in fuzzy logic based on Detection of Consequent Formulas algorithm. It is possible to combine it with the standard proof search techniques like breadth-first search or linear search. The thesis also includes algorithms and implementation of the presented inference rules and the resolution strategies.

Abstract:

The thesis presents refutational resolution theorem proving system for both the classical and many-valued logics based on the general (non-clausal) resolution rule. There is also presented a unification algorithm handling existentiality without the need of skolemization. This formalism integrates properties especially suitable for description logic and for fuzzy predicate logic. The problem of automated reasoning concerning fuzzy logic requires more complex methods in contrast to classical logic. Presented formalism overcomes the key unsolvable obstacle - clausal normal form generation (in fuzzy logic) - by introduction of generally applicable inference rule (working with general formulas not only clauses). Additionally we present several inference strategies for efficient theorem proving in fuzzy logic based on Detection of Consequent Formulas algorithm. It is possible to combine it with the standard proof search techniques like breadth-first search or linear search. The thesis also includes algorithms and implementation of the presented inference rules and the resolution strategies.

Keywords

formální logické sytémy, neklauzulární rezoluce

Language used: Czech

Date on which the thesis was submitted / produced: 30. 6. 2007

Accessible from:: 30. 6. 2007

Thesis defence

• Date of defence: 28. 8. 2007
• Supervisor: prof. RNDr. Alena Lukasová, CSc.

University of Ostrava

Faculty of Science

Doctoral programme / field:
Information Science / Information Systems