Интуитивная семантика для релевантного следования


D.V. Zaitsev


In this paper I return an old but fruitful idea suggested independently by J.M. Dunn and E.K. Voishvillo of true (relevant) entailment as a relation between premisses and conclusion when an information contained in conclusion as a part of information contained in premisses. In so doing I consider Belnap’s famous logical and approximation lattices that form bilattice FOUR and prove that informational semantics for first-degree entailment can be developed on the basis of approximation lattice taken alone.






Войшвилло Е.К. Семантика релевантной логики и вопрос о природе логических законов // Разум и культура. Труды международного франко-советского коллоквиума. Лилль, 26-29 апреля 1978 г. М., 1983.
Войшвилло Е.К. Философско-методологические аспекты релевантной логики. М., 1988.
Войшвилло Е.К., Дегтярев М.Г. Логика как часть теории познания и научной методологии (фундаментальный курс), Кн. I. М., 1994.
Arieli О. and Avron A. Logical bilattices. and inconsistent data // Proceedings 9th IEEE Annual Symposium on Logic in Computer Science, IEEE Press, 1994. P. 468-476.
Arieli O. and Avron A. Reasoning with logical bilattices // Journal of Logic, Language and Information. 1996. Vol. 5, P. 25-63.
Avron A. The structure of interlaced bilattices // Mathematical Structures in Computer Science. 1996. Vol. 6. P. 287-299.
Belnap N.D. A useful four-valued logic // J.M. Dunn and G. Epstein (eds.), Modern Uses of Multiple-Valued Logic,, D‘. Reidel Publishing Company, Dordrecht, 1977.
Belnap N.D. How a computer should: think // G. Ryle (ed.), Contemporary Aspects of Philosophy, Oriel Press Ltd., Stocksfield, 1977. P. 30-55.
Dunn J.M. The algebra of intensional logics, Doctoral Dissertation, University of Pittsburgh, Ann Arbor, 1966 (University Microfilms).
Dunn J.M. An intuitive semantics for first, degree relevant implications (abstract) // The Journal of Symbolic Logic. Vol. 36. P. 362-363.
Dunn J.M. Intuitive semantics for first-degree entailment and ‘coupled trees’ // Philosophical Studies. 1976. Vol. 29.
Fitting M. Bilattices and the theory of truth // Journal of Philosophical Logic. 1989. Vol. 18. P. 225-256.
Fitting M. Bilattices in logic programming // in G. Epstein (ed.), The Twentieth International Symposium on Multiple-Valued Logic, IEEE Press, 1990. P. 238-246.
Fitting M. Bilattices and the semantics of logic programming // Journal of Logic Programming. 1991. Vol. 11. P. 91-116.
Fitting М. Bilattices are nice things //in V.F. Hendricks, S.A. Pedersen and T. Bolander (eds.), Self-Reference, CSLI Publications, Cambridge University Press, 2004.
Ginsberg M. Multi-valued logics, in Proceedings of AAAI-86 // Fifth National Conference on Artificial Intellegence, Morgan Kaufman Publishers, Los Altos, 1986. P. 243-247.
Ginsberg M. Multivalued logics: A uniform approach to reasoning // AI, Computer Intelligence. 1988. VoL 4. P. 256-316.
Shramko Y., and Wansing H. Some useful sixteen-valued logics: How a computer network should think // Journal of Philosophical Logic. 2005. Vol. 34.