http://hdl.handle.net/11089/31471 2026-04-06T20:39:22Z 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. 2019-12-31T00:00:00Z 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. 2019-12-31T00:00:00Z 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. 2019-12-31T00:00:00Z 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