On Belnapian modal algebras: Representations, homomorphisms, congruences, and so on

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On Belnapian modal algebras: Representations, homomorphisms, congruences, and so on

Siberian Electronic Mathematical Reports. 2013. Vol. 10. P. 517–534.

We obtain a bunch of principal results on Belnapian modal algebras (henceforth called BK-lattices) — these results may serve as a semantical basis for further investigation of the lattice of extensions of Belnapian modal logic (denoted by BK here).

Language: English

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The lattice of Belnapian modal logics: Special extensions and counterparts

Speranski S. O., Logic and Logical Philosophy 2016 Vol. 25 No. 1 P. 3–33

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 (or rather sublattices) of so-called explosive, complete and classical Belnapian modal logics; assigning to every normal modal logic three special ...

Added: December 27, 2025

Belnap–Dunn modal logics: Truth constants vs. truth values

Odintsov S., Speranski S. O., Review of Symbolic Logic 2020 Vol. 13 No. 2 P. 416–435

We shall be concerned with the modal logic BK — which is based on the Belnap–Dunn four-valued matrix, and can be viewed as being obtained from the least normal modal logic K by adding ‘strong negation’. Though all four values ‘truth’, ‘falsity’, ‘neither’ and ‘both’ are employed in its Kripke semantics, only the first two are ...

Added: December 26, 2025

Hintikka's independence-friendly logic meets Nelson's realizability

Odintsov S., Speranski S. O., Shevchenko I., Studia Logica 2018 Vol. 106 No. 3 P. 637–670

Inspired by Hintikka’s ideas on constructivism, we are going to ‘effectivize’ the game-theoretic semantics (abbreviated GTS) for independence-friendly first-order logic (IF-FOL), but in a somewhat different way than he did in the monograph ‘The Principles of Mathematics Revisited’. First we show that Nelson’s realizability interpretation — which extends the famous Kleene’s realizability interpretation by adding ...

Added: December 26, 2025

Products of modal logics and tensor products of modal algebras

Gabbay D., Shapirovsky I., Shehtman V. B., Journal of Applied Logic 2014 Vol. 12 No. 4 P. 570–583

One of natural combinations of Kripke complete modal logics is the product, an operation that has been extensively investigated over the last 15 years. In this paper we consider its analogue for arbitrary modal logics: to this end, we use product-like constructions on general frames and modal algebras. This operation was first introduced by Y. ...

Added: March 24, 2015

L'opposition: analyse sémantique d'une notion flottante

Schang F., (France) 2012 Vol. 13 P. 65–85

A logical theory of oppositions deals with the relation between propositions and their truth values. On the basis of a formal semantics that proceeds by means of questions-answers, three theses are claimed in the following: (1) the concept of opposition usually refers to incompatibility, but our logical analysis focusses upon a broader relation of difference; ...

Added: October 31, 2014