Bulletin of the Section of Logic 46/1-2 (2017)
http://hdl.handle.net/11089/24277
2024-03-02T17:58:13ZInvolutive Nonassociative Lambek Calculus: Sequent Systems and Complexity
http://hdl.handle.net/11089/24563
Involutive Nonassociative Lambek Calculus: Sequent Systems and Complexity
Buszkowski, Wojciech
In [5] we study Nonassociative Lambek Calculus (NL) augmented with De Morgan negation, satisfying the double negation and contraposition laws. This logic, introduced by de Grooté and Lamarche [10], is called Classical Non-Associative Lambek Calculus (CNL). Here we study a weaker logic InNL, i.e. NL with two involutive negations. We present a one-sided sequent system for InNL, admitting cut elimination. We also prove that InNL is PTIME.
2017-01-01T00:00:00ZSome Weak Variants of the Existence and Disjunction Properties in Intermediate Predicate Logics
http://hdl.handle.net/11089/24564
Some Weak Variants of the Existence and Disjunction Properties in Intermediate Predicate Logics
Suzuki, Nobu-Yuki
We discuss relationships among the existence property, the disjunction property, and their weak variants in the setting of intermediate predicate logics. We deal with the weak and sentential existence properties, and the Z-normality, which is a weak variant of the disjunction property. These weak variants were presented in the author’s previous paper [16]. In the present paper, the Kripke sheaf semantics is used.
2017-01-01T00:00:00ZOn Theses Without Iterated Modalities of Modal Logics Between C1 and S5. Part 1
http://hdl.handle.net/11089/24565
On Theses Without Iterated Modalities of Modal Logics Between C1 and S5. Part 1
Pietruszczak, Andrzej
This is the first, out of two papers, in which we identify all logics between C1 and S5 having the same theses without iterated modalities. All these logics canbe divided into certain groups. Each such group depends only on which of thefollowing formulas are theses of all logics from this group: (N), (T), (D), ⌜(T)∨ ☐q⌝,and for any n 0 a formula ⌜(T) ∨ (altn)⌝, where (T) has not the atom ‘q’, and(T) and (altn) have no common atom. We generalize Pollack’s result from [12],where he proved that all modal logics between S1 and S5 have the same theseswhich does not involve iterated modalities (i.e., the same first-degree theses).
2017-01-01T00:00:00ZFrom Gentzen to Jaskowski and Back: Algorithmic Translation of Derivations Between the Two Main Systems of Natural Deduction
http://hdl.handle.net/11089/24562
From Gentzen to Jaskowski and Back: Algorithmic Translation of Derivations Between the Two Main Systems of Natural Deduction
von Plato, Jan
The way from linearly written derivations in natural deduction, introduced by Jaskowski and often used in textbooks, is a straightforward root-first translation. The other direction, instead, is tricky, because of the partially ordered assumption formulas in a tree that can get closed by the end of a derivation. An algorithm is defined that operates alternatively from the leaves and root of a derivation and solves the problem.
2017-01-01T00:00:00Z