http://hdl.handle.net/11089/9984 Sun, 05 Apr 2026 22:55:20 GMT 2026-04-05T22:55:20Z https://dspace.uni.lodz.pl:443/bitstream/id/4aa442f1-35eb-4598-bcbe-da8e97054f41/ http://hdl.handle.net/11089/9984 http://hdl.handle.net/11089/17400 Categorical Abstract Algebraic Logic: Referential π-Institutions Voutsadakis, George Wójcicki introduced in the late 1970s the concept of a referential semantics for propositional logics. Referential semantics incorporate features of the Kripke possible world semantics for modal logics into the realm of algebraic and matrix semantics of arbitrary sentential logics. A well-known theorem of Wójcicki asserts that a logic has a referential semantics if and only if it is selfextensional. Referential semantics was subsequently studied in detail by Malinowski and the concept of selfextensionality has played, more recently, an important role in the field of abstract algebraic logic in connection with the operator approach to algebraizability. We introduce and review some of the basic definitions and results pertaining to the referential semantics of π-institutions, abstracting corresponding results from the realm of propositional logics. Thu, 01 Jan 2015 00:00:00 GMT http://hdl.handle.net/11089/17400 2015-01-01T00:00:00Z http://hdl.handle.net/11089/17399 Closure Operators on Complete Almost Distributive Lattices-III Rao, Calyampudi Radhakrishna; Undurthi, Venugopalam In this paper, we prove that the lattice of all closure operators of a complete Almost Distributive Lattice L with fixed maximal element m is dual atomistic. We define the concept of a completely meet-irreducible element in a complete ADL and derive a necessary and sufficient condition for a dual atom of Φ(L) to be complemented. Thu, 01 Jan 2015 00:00:00 GMT http://hdl.handle.net/11089/17399 2015-01-01T00:00:00Z http://hdl.handle.net/11089/17398 An Observation Concerning Porte’s Rule in Modal Logic French, Rohan; Humberstone, Lloyd It is well known that no consistent normal modal logic contains (as theorems) both ◊A and ◊¬A (for any formula A). Here we observe that this claim can be strengthened to the following: for any formula A, either no consistent normal modal logic contains ◊A, or else no consistent normal modal logic contains ◊¬A. Thu, 01 Jan 2015 00:00:00 GMT http://hdl.handle.net/11089/17398 2015-01-01T00:00:00Z http://hdl.handle.net/11089/17397 Non-Fregean Logics of Analytic Equivalence (II) Biłat, Andrzej This paper presents the main assumptions of Andrzej Grzegorczyk’s last research project concerning the logic of synonymity. It shows that the basis of logic of analytic equivalence, presented in the first part of the work, fully corresponds with these assumptions. Thu, 01 Jan 2015 00:00:00 GMT http://hdl.handle.net/11089/17397 2015-01-01T00:00:00Z