- Tytuł:
- Four-valued expansions of Dunn-Belnaps logic (I): Basic characterizations
- Autorzy:
- Pynko, Alexej P.
- Powiązania:
- https://bibliotekanauki.pl/articles/1023300.pdf
- Data publikacji:
- 2020-12-30
- Wydawca:
- Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
- Tematy:
-
propositional logic
logical matrix
Dunn-Belnap's logic
expansion
[bounded] distributive/De Morgan lattice
equality determinant - Opis:
- Basic results of the paper are that any four-valued expansion L4 of Dunn-Belnap's logic DB4 is de_ned by a unique (up to isomorphism) conjunctive matrix ℳ4 with exactly two distinguished values over an expansion 4 of a De Morgan non-Boolean four-valued diamond, but by no matrix with either less than four values or a single [non-]distinguished value, and has no proper extension satisfying Variable Sharing Property (VSP). We then characterize L4's having a theorem / inconsistent formula, satisfying VSP and being [inferentially] maximal / subclassical / maximally paraconsistent, in particular, algebraically through ℳ4|4's (not) having certain submatrices|subalebras. Likewise, [providing 4 is regular / has no three-element subalgebra] L4 has a proper consistent axiomatic extension if[f] ℳ4 has a proper paraconsistent / two-valued submatrix [in which case the logic of this submatrix is the only proper consistent axiomatic extension of L4 and is relatively axiomatized by the Excluded Middle law axiom]. As a generic tool (applicable, in particular, to both classically-negative and implicative expansions of DB4), we also prove that the lattice of axiomatic extensions of the logic of an implicative matrix ℳ with equality determinant is dual to the distributive lattice of lower cones of the set of all submatrices of ℳ with non-distinguished values.
- Źródło:
-
Bulletin of the Section of Logic; 2020, 49, 4; 401-437
0138-0680
2449-836X - Pojawia się w:
- Bulletin of the Section of Logic
- Dostawca treści:
- Biblioteka Nauki
Artykuł