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Disjunctive Multiple-Conclusion Consequence Relations

100%

Nowak M.

Bulletin of the Section of Logic

2019

tom 48

nr 4

The concept of multiple-conclusion consequence relation from [8] and [7] is considered. The closure operation C assigning to any binary relation r (dened on the power set of a set of all formulas of a given language) the least multiple-conclusion consequence relation containing r, is dened on the grounds of a natural Galois connection. It is shown that the very closure C is an isomorphism from the power set algebra of a simple binary relation to the Boolean algebra of all multiple-conclusion consequence relations.

A Syntactic Approach to Closure Operation

100%

Nowak M.

Bulletin of the Section of Logic

2017

tom 46

nr 3/4

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.

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2 Bulletin of the Section of Logic

2 Nowak M.

1 2019

1 2017

Wyniki wyszukiwania

Disjunctive Multiple-Conclusion Consequence Relations

A Syntactic Approach to Closure Operation