Satisfiability in many-valued sentential logic is NP-complete

Many-valued Horn Logic is Hard

Fuzzy Description Logics (FDLs) have been introduced to reason about vague or imprecise knowledge in application domains. In recent years, reasoning in many FDLs based on infinitely many values has been proved to be undecidable [3,15] and systematic studies have been undertaken on this topic [8]. On the other hand, every finite-valued FDL that has been studied in the recent literature has not o...

Many-Valued Complete Distributivity

Suppose (Ω, ∗, I) is a commutative, unital quantale. Categories enriched over Ω can be studied as generalized, or many-valued, ordered structures. Because many concepts, such as complete distributivity, in lattice theory can be characterized by existence of certain adjunctions, they can be reformulated in the many-valued setting in terms of categorical postulations. So, it is possible, by aid o...

A complete many-valued logic with product-conjunction

A simplified NP-complete satisfiability problem

Cook [l] has shown that 3-SAT, the Boolean satisfiability problem restricted to instances with exactly three variables per clause, is NP-complete. This is a tightest possible restriction on the number of variables in a clause because as Even et al. [2] demonstrate, 2-SAT is in P. Horowitz and Sahni [5] point up the importance of finding the strongest possible restrictions under which a problem ...

Many-valued hybrid logic

In this paper we define a many-valued semantics for hybrid logic and we give a sound and complete tableau system which is prooftheoretically well-behaved, in particular, it gives rise to a decision procedure for the logic. This shows that many-valued hybrid logics is a natural enterprise and opens up the way for future applications.