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Number 49

2014 Next

Publication date: 11.09.2014

Licence: None

Editorial team

Editors Paweł M. Idziak, Andrzej Wroński

Issue content

Norihiro Kamide

Reports on Mathematical Logic, Number 49, 2014, pp. 3-21

https://doi.org/10.4467/20842589RM.14.001.2271
It is known that many-valued paraconsistent logics are useful for expressing uncertain and inconsistency-tolerant reasoning in a wide range of Computer Science. Some four-valued and sixteen-valued logics have especially been well-studied. Some four-valued logics are not so fine-grained, and some sixteen-valued logics are enough fine-grained, but rather complex. In this paper, a natural eight-valued paraconsistent logic rather than four-valued and sixteen-valued logics is introduced as a Gentzen-type sequent calculus. This eight-valued logic is enough fine-grained and simpler than sixteen-valued logic. A triplet valuation semantics is introduced for this logic, and the completeness theorem for this semantics is proved. The cut-elimination theorem for this logic is proved, and this logic is shown to be decidable.
 
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Rafael Grimson, Bart Kuijpers

Reports on Mathematical Logic, Number 49, 2014, pp. 23-34

https://doi.org/10.4467/20842589RM.14.002.2272
We consider the 10-fragment of second-order logic over the vocabulary h+;; 0; 1; <; S1; :::; Ski, interpreted over the reals, where the predicate symbols Si are interpreted as semialgebraic sets. We show that, in this context, satis ability of formulas is decidable for the rst-order 9-quanti er fragment and undecidable for the 98- and 8-fragments. We also show that for these three fragments the same (un)decidability results hold for containment and equivalence of formulas.
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Grzegorz Jagiella, Ludomir Newelski

Reports on Mathematical Logic, Number 49, 2014, pp. 35-46

https://doi.org/10.4467/20842589RM.14.003.2273

We investigate minimal rst-order structures and consider interpretability and de nability of orderings on them. We also prove the minimality of their canonical substructures.

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Sergio A. Celani, Daniela Montangie

Reports on Mathematical Logic, Number 49, 2014, pp. 47-77

https://doi.org/10.4467/20842589RM.14.004.2274

We introduce the variety of Hilbert algebras with a modal operator , called H-algebras. The variety of H-algebras is the algebraic counterpart of the f!;g-fragment of the intuitionitic modal logic IntK. We will study the theory of representation and we will give a topological duality for the variety of H-algebras. We are going to use these results to prove that the basic implicative modal logic IntK! and some axiomatic extensions are canonical. We shall also to determine the simple and subdirectly irreducible algebras in some subvarieties of H-algebras.

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Jerzy Mycka

Reports on Mathematical Logic, Number 49, 2014, pp. 79-97

https://doi.org/10.4467/20842589RM.14.005.2275

We will introduce the special kind of the order relations into recursively enumerable sets and prove that they can be used to distinguish (albeit in a non-constructive way) between recursive and non-recursive sets.

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Grzegorz Herman

Reports on Mathematical Logic, Number 49, 2014, pp. 99-117

https://doi.org/10.4467/20842589RM.14.006.2276

We study the problem of deciding, whether a given partial order is embeddable into two consecutive layers of a Boolean lattice. Employing an equivalent condition for such em- beddability similar to the one given by J. Mittas and K. Reuter [5], we prove that the decision problem is NP-complete by showing a polynomial-time reduction from the not-all-equal variant of the Satis ability problem.

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