Name
Abstract | ||
|---|---|---|
Product Logic Π is an axiomatic extension of Hájek's Basic Fuzzy Logic BL coping with the 1-tautologies when the strong conjunction & and implication → are interpreted by the product of reals in [0, 1] and its residuum respectively. In this paper we investigate expansions of Product Logic by adding into the language a countable set of truth-constants (one truth-constant for each r in a countable Π-subalgebra of [0, 1]) and by adding the corresponding book-keeping axioms for the truthconstants. We first show that the corresponding logics Π() are algebraizable, and hence complete with respect to the variety of Π()-algebras. The main result of the paper is the canonical standard completeness of these logics, that is, theorems of Π() are exactly the 1-tautologies of the algebra defined over the real unit interval where the truth-constants are interpreted as their own values. It is also shown that they do not enjoy the canonical strong standard completeness, but they enjoy it for finite theories when restricted to evaluated Π-formulas of the kind → ψ, where is a truth-constant and ψ a formula not containing truth-constants. Finally we consider the logics ΠΔ(), the expansion of Π() with the well-known Baaz's projection connective Δ, and we show canonical finite strong standard completeness for them. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1093/logcom/exi075 | J. Log. Comput. |
Keywords | Field | DocType |
product logic,canonical strong standard completeness,truth-constants,corresponding book-keeping axiom,non-classical logic,fuzzy logic,basic fuzzy logic bl,strong conjunction,standard completeness,corresponding logic,canonical standard completeness,finite strong standard completeness,finite theory,axiomatic extension,non classical logic | T-norm fuzzy logics,Discrete mathematics,Countable set,Non-classical logic,Algorithm,Unit interval,Classical logic,Monoidal t-norm logic,Many-valued logic,Intermediate logic,Mathematics | Journal |
Volume | Issue | ISSN |
16 | 2 | 0955-792X |
Citations | PageRank | References |
24 | 1.37 | 10 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Petr Savický | 1 | 328 | 34.36 |
| Roberto Cignoli | 2 | 415 | 52.03 |
| Francesc Esteva | 3 | 1885 | 200.14 |
| Lluís Godo | 4 | 888 | 56.28 |
| Carles Noguera | 5 | 462 | 33.93 |