A Syntactic Approach to Closure Operation

• Autorzy: Marek Nowak
• Języki publikacji: EN

Abstrakty

EN

In the paper, tracing the traditional Hilbert-style syntactic account of logics, a syntactic characteristic of a closure operation defined on a complete lattice follows. The approach is based on observation that the role of rule of inference for a given consequence operation may be played by an ordinary binary relation on the complete lattice on which the closure operation is defined.

Słowa kluczowe

EN

closure operation; closure system; rule of inference

• Wydawca: Wydawnictwo Uniwersytetu Łódzkiego
• Czasopismo: Bulletin of the Section of Logic
• Rocznik: 2017
• Tom: 46
• Numer: 3/4

Daty

wydano

2017-12-30

Twórcy

autor

Marek Nowak

• Department of Logic, University of Lodz Lindleya 3/5, 90-131 Lódź, Poland

Bibliografia

• [1] T. S. Blyth, Lattices and Ordered Algebraic Structures, Springer (2005).
• [2] K. Denecke, M. Erné, S. L. Wismath (eds.), Galois Connections and Applications, Kluwer (2004).
• [3] F. Domenach, B. Leclerc, Biclosed binary relations and Galois connections, Order 18 (2001), pp. 89–104.
• [4] M. Erné, J. Koslowski, A. Melton, G. E. Strecker, A Primer on Galois Connections, Annals of the New York Academy of Sciences, vol. 704 (1993), pp. 103–125.
• [5] D. J. Shoesmith, T. J. Smiley, Multiple-conclusion Logic, Cambridge University Press (1978).
• [6] R. Wójcicki, Lectures on Propositional Calculi, Ossolineum (1984).
• [7] R. Wójcicki, Theory of Logical Calculi. Basic Theory of Consequence Operations, Kluwer (1988).
• [8] J. Zygmunt, An Essay in Matrix Semantics for Consequence Relations, Wydawnictwo Uniwersytetu Wrocławskiego, Wrocław (1984).

Identyfikatory

DOI

10.18778/0138-0680.46.3.4.04