Expanding Belnap: dualities for a new class of default bilattices

Craig, Andrew, P. K. Expanding Belnap: dualities for a new class of default bilattices / Andrew P. K. Craig, Brian A. Davey, Miroslav Haviar. -- Bilattices provide an algebraic tool with which to model simultaneously knowledge and truth. They were introduced by Belnap in 1977 in a paper entitled How a computer should think. Belnap argued that instead of using a logic with two values, for ‘true’ and ‘false’, a computer should use a logic with two further values, for ‘contradiction’ and ‘no information´. The resulting structure is equipped with two lattice orders, a knowledge order and a truth order, and hence is called a bilattice. Prioritised default bilattices include not only values for ‘true’, ‘false’, ‘contradiction’ and ‘no information’, but also indexed families of default values for simultaneous modelling of degrees of knowledge and truth. We focus on a new family of prioritised default bilattices: Jn, for all natural numbers n. The bilattice J0 is precisely Belnap’s seminal example. We obtain a multisorted duality for the variety generated by Jn, and separately a single sorted duality for the quasivariety generated by Jn. The main tool for both dualities is a unified approach that enables us to identify the meet-irreducible elements of the appropriate subuniverse lattices. Our results provide an interesting example where the multi-sorted duality for the variety has a simpler structure than the single-sorted duality for the quasivariety

In Algebra universalis. -- Basel : Springer Nature Switzerland AG, 2020. -- ISSN 0002-5240. -- ISSN 1420-8911. -- Vol. 81, no. 4 (2020), pp. 1-26

1. natural duality 2. výsledky 3. algebras 4. články

I. Davey, Brian A.
II. Haviar, Miroslav, 1965-
III. Algebra universalis. -- Vol. 81, no. 4 (2020), pp. 1-26
BB301