Bulletin of the Section of Logic 48/4 (2019)
http://hdl.handle.net/11089/31471
2024-06-13T11:33:53ZDisjunctive Multiple-Conclusion Consequence Relations
http://hdl.handle.net/11089/35368
Disjunctive Multiple-Conclusion Consequence Relations
Nowak, Marek
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.
2019-12-31T00:00:00ZTwo Treatments of Definite Descriptions in Intuitionist Negative Free Logic
http://hdl.handle.net/11089/35367
Two Treatments of Definite Descriptions in Intuitionist Negative Free Logic
Kurbis, Nils
Sentences containing definite descriptions, expressions of the form `The F', can be formalised using a binary quantier that forms a formula out of two predicates, where ℩x[F;G] is read as `The F is G'. This is an innovation over the usual formalisation of definite descriptions with a term forming operator. The present paper compares the two approaches. After a brief overview of the system INF℩ of intuitionist negative free logic extended by such a quantier, which was presented in [4], INF℩ is first compared to a system of Tennant's and an axiomatic treatment of a term forming ℩ operator within intuitionist negative free logic. Both systems are shown to be equivalent to the subsystem of INF℩ in which the G of ℩x[F;G] is restricted to identity. INF℩ is then compared to an intuitionist version of a system of Lambert's which in addition to the term forming operator has an operator for predicate abstraction for indicating scope distinctions. The two systems will be shown to be equivalent through a translation between their respective languages. Advantages of the present approach over the alternatives are indicated in the discussion.
2019-12-31T00:00:00ZAn Investigation into Intuitionistic Logic with Identity
http://hdl.handle.net/11089/35365
An Investigation into Intuitionistic Logic with Identity
Chlebowski, Szymon; Leszczyńska-Jasion, Dorota
We define Kripke semantics for propositional intuitionistic logic with Suszko’s identity (ISCI). We propose sequent calculus for ISCI along with cut-elimination theorem. We sketch a constructive interpretation of Suszko’s propositional identity connective.
2019-12-31T00:00:00ZMany Faces of Lattice Tolerances
http://hdl.handle.net/11089/35366
Many Faces of Lattice Tolerances
Grygiel, Joanna
Our aim is to overview and discuss some of the most popular approaches to the notion of a tolerance relation in algebraic structures with the special emphasis on lattices.
2019-12-31T00:00:00Z