http://hdl.handle.net/11089/30219 Wed, 08 Apr 2026 12:53:22 GMT 2026-04-08T12:53:22Z https://dspace.uni.lodz.pl:443/bitstream/id/7ec1afc2-3a15-45a7-96ce-8acacf583a7d/ http://hdl.handle.net/11089/30219 http://hdl.handle.net/11089/30602 Full Cut Elimination and Interpolation for Intuitionistic Logic with Existence Predicate Maffezioli, Paolo; Orlandelli, Eugenio In previous work by Baaz and Iemhoff, a Gentzen calculus for intuitionistic logic with existence predicate is presented that satisfies partial cut elimination and Craig's interpolation property; it is also conjectured that interpolation fails for the implication-free fragment. In this paper an equivalent calculus is introduced that satisfies full cut elimination and allows a direct proof of interpolation via Maehara's lemma. In this way, it is possible to obtain much simpler interpolants and to better understand and (partly) overcome the failure of interpolation for the implication-free fragment. Tue, 01 Jan 2019 00:00:00 GMT http://hdl.handle.net/11089/30602 2019-01-01T00:00:00Z http://hdl.handle.net/11089/30601 Semi-Heyting Algebras and Identities of Associative Type Cornejo, Juan M.; Sankappanavar, Hanamantagouda P. An algebra A = ⟨A, ∨, ∧, →, 0, 1⟩ is a semi-Heyting algebra if ⟨A, ∨, ∧, 0, 1⟩ is a bounded lattice, and it satisfies the identities: x ∧ (x → y) ≈ x ∧ y, x ∧ (y → z) ≈ x ∧ [(x ∧ y) → (x ∧ z)], and x → x ≈ 1. SH denotes the variety of semi-Heyting algebras. Semi-Heyting algebras were introduced by the second author as an abstraction from Heyting algebras. They share several important properties with Heyting algebras. An identity of associative type of length 3 is a groupoid identity, both sides of which contain the same three (distinct) variables that occur in any order and that are grouped in one of the two (obvious) ways. A subvariety of SH is of associative type of length 3 if it is defined by a single identity of associative type of length 3. In this paper we describe all the distinct subvarieties of the variety SH of asociative type of length 3. Our main result shows that there are 3 such subvarities of SH. Tue, 01 Jan 2019 00:00:00 GMT http://hdl.handle.net/11089/30601 2019-01-01T00:00:00Z http://hdl.handle.net/11089/30600 The Method of Socratic Proofs Meets Correspondence Analysis Leszczyńska-Jasion, Dorota; Petrukhin, Yaroslav; Shangin, Vasilyi The goal of this paper is to propose correspondence analysis as a technique for generating the so-called erotetic (i.e. pertaining to the logic of questions) calculi which constitute the method of Socratic proofs by Andrzej Wiśniewski. As we explain in the paper, in order to successfully design an erotetic calculus one needs invertible sequent-calculus-style rules. For this reason, the proposed correspondence analysis resulting in invertible rules can constitute a new foundation for the method of Socratic proofs. Correspondence analysis is Kooi and Tamminga's technique for designing proof systems. In this paper it is used to consider sequent calculi with non-branching (the only exception being the rule of cut), invertible rules for the negation fragment of classical propositional logic and its extensions by binary Boolean functions. Tue, 01 Jan 2019 00:00:00 GMT http://hdl.handle.net/11089/30600 2019-01-01T00:00:00Z http://hdl.handle.net/11089/30599 A Binary Quantifier for Definite Descriptions in Intuitionist Negative Free Logic: Natural Deduction and Normalisation Kurbis, Nils This paper presents a way of formalising definite descriptions with a binary quantifier ℩, where ℩x[F, G] is read as `The F is G'. Introduction and elimination rules for ℩ in a system of intuitionist negative free logic are formulated. Procedures for removing maximal formulas of the form ℩x[F, G] are given, and it is shown that deductions in the system can be brought into normal form. Tue, 01 Jan 2019 00:00:00 GMT http://hdl.handle.net/11089/30599 2019-01-01T00:00:00Z