Citations of:
Add citations
You must login to add citations.


In this paper we give an analytic tableau calculus P L 1 6 for a functionally complete extension of Shramko and Wansing’s logic. The calculus is based on signed formulas and a single set of tableau rules is involved in axiomatising each of the four entailment relations ⊧ t, ⊧ f, ⊧ i, and ⊧ under consideration—the differences only residing in initial assignments of signs to formulas. Proving that two sets of formulas are in one of the first three entailment (...) 

Let K be the least normal modal logic and BK its Belnapian version, which enriches K with ‘strong negation’. We carry out a systematic study of the lattice of logics containing BK based on: • introducing the classes of socalled explosive, complete and classical Belnapian modal logics; • assigning to every normal modal logic three special conservative extensions in these classes; • associating with every Belnapian modal logic its explosive, complete and classical counterparts. We investigate the relationships between special extensions (...) 

Earlier algebraic semantics for Belnapian modal logics were defined in terms of twiststructures over modal algebras. In this paper we introduce the class of BK lattices, show that this class coincides with the abstract closure of the class of twiststructures, and it forms a variety. We prove that the lattice of subvarieties of the variety of BK lattices is dually isomorphic to the lattice of extensions of Belnapian modal logic BK . Finally, we describe invariants determining a twiststructure over a (...) 

We explore a possibility of generalization of classical truth values by distinguishing between their ontological and epistemic aspects and combining these aspects within a joint semantical framework. The outcome is four generalized classical truth values implemented by Cartesian product of two sets of classical truth values, where each generalized value comprises both ontological and epistemic components. This allows one to define two unary twin connectives that can be called “semiclassical negations”. Each of these negations deals only with one of the (...) 

Antirealistic conceptions of truth and falsity are usually epistemic or inferentialist. Truth is regarded as knowability, or provability, or warranted assertability, and the falsity of a statement or formula is identified with the truth of its negation. In this paper, a noninferentialist but nevertheless antirealistic conception of logical truth and falsity is developed. According to this conception, a formula (or a declarative sentence) A is logically true if and only if no matter what is told about what is told about (...) 

Multialgebras (or hyperalgebras or nondeterministic algebras) have been much studied in mathematics and in computer science. In 2016 Carnielli and Coniglio introduced a class of multialgebras called swap structures, as a semantic framework for dealing with several Logics of Formal Inconsistency (or LFIs) that cannot be semantically characterized by a single finite matrix. In particular, these LFIs are not algebraizable by the standard tools of abstract algebraic logic. In this paper, the first steps towards a theory of nondeterministic algebraization of (...) 

In a recent paper we have defined an analytic tableau calculus PL_16 for a functionally complete extension of Shramko and Wansing's logic based on the trilattice SIXTEEN_3. This calculus makes it possible to define syntactic entailment relations that capture central semantic relations of the logicsuch as the relations =_t, =_f, and =_i that each correspond to a lattice order in SIXTEEN_3; and =, the intersection of =_t and =_f,. / It turns out that our method of characterising these semantic relationsas (...) 

In this paper, biintuitionistic multilattice logic, which is a combination of multilattice logic and the biintuitionistic logic also known as Heyting–Brouwer logic, is introduced as a Gentzentype sequent calculus. A Kripke semantics is developed for this logic, and the completeness theorem with respect to this semantics is proved via theorems for embedding this logic into biintuitionistic logic. The logic proposed is an extension of firstdegree entailment logic and can be regarded as a biintuitionistic variant of the original classical multilattice logic (...) 

Sequent calculi for trilattice logics, including those that are determined by the truth entailment, the falsity entailment and their intersection, are given. This partly answers the problems in ShramkoWansing. 

A sequent calculus for Odintsov’s Hilbertstyle axiomatization of a logic related to the trilattice SIXTEEN3 of generalized truth values is introduced. The completeness theorem w.r.t. a simple semantics for is proved using Maehara’s decomposition method that simultaneously derives the cutelimination theorem for . A firstorder extension of and its semantics are also introduced. The completeness and cutelimination theorems for are proved using Schütte’s method. 

The trilattice SIXTEEN3 introduced in Shramko & Wansing (2005) is a natural generalization of the famous bilattice FOUR2. Some Hilbertstyle proof systems for trilattice logics related to SIXTEEN3 have recently been studied (Odintsov, 2009; Shramko & Wansing, 2005). In this paper, three sequent calculi GB, FB, and QB are presented for Odintsovs coordinate valuations associated with valuations in SIXTEEN3. The equivalence between GB, FB, and QB, the cutelimination theorems for these calculi, and the decidability of B are proved. In addition, (...) 