In this paper we study some fragments without implications of the (Hilbert) full Lambek logic HFL and also some fragments without implications of some of the substructural extensions of that logic. To do this, we perform an algebraic analysis of the Gentzen systems defined by the substructural calculi FLσ. Such systems are extensions of the full Lambek calculus FL with the rules codified by a s...

The variety of semantical approaches that have been invented for logic programs for reasoning about inconsistent databases is quite broad. Especially, we are interested in an ontological encapsulation of a many-valued logics with negation, based on bilattices, into a 2-valued logic: this new approach is a minimilistic one based on the concept of the semantic reflection. We define a Model theore...

a controversy among the muslim philosophers about the domain of the extensions was that is the subject of the verity-propositions contained the impossible extensions or only all of the actual and possible ones. from ibn-sina to al-khunaji, there are explicit texts to the former view; but later logicians, starting with athir al-din al-abhari, were inclined to the latter. in this paper, we attamp...

We introduce probabilistic many-valued logic programs in which the implication connective is interpreted as material implication. We show that probabilistic many-valued logic programming is computationally more complex than classical logic programming. More precisely, some deduction problems that are P-complete for classical logic programs are shown to be co-NP-complete for probabilistic many-v...

To express wider uncertainty, B?hounek and Da?ková studied fuzzy partial logic function. At the same time, Borzooei generalized t-norms put forward concept of when studying lattice valued quantum effect algebras. Based on t-norms, Zhang et al. residuated implications (PRIs) proposed lattices (PRLs). In this paper, we mainly study related algebraic structure logic. First, provide definitions reg...

It is natural to ask under what conditions negating a conditional is equivalent to negating its consequent. Given a bivalent background logic, this is equivalent to asking about the conjunction of Conditional Excluded Middle (CEM, opposite conditionals are not both false) and Weak Boethius’ Thesis (WBT, opposite conditionals are not both true). In the system CI.0 of consequential implication, w...

Many practical problems involve constraints in 0-1 variables. We apply the constraint logic programming language CLP(PB) to model and reason about 0-1 problems. Given a set of possibly non-linear 0-1 constraints, the solver of CLP(PB) computes an equivalent set of extended clauses. By exploiting the metaprogramming facilities of the logic programming environment, we are able to deal with arbitr...

Intuitionistic logic programming provides the notion of embedded implication in rule bodies, which can be used to reason about a current database modified by the antecedent. This can be applied to a system that translates SQL to Datalog to solve SQL WITH queries, for which relations are locally defined and can therefore be understood as added to the current database. In addition, assumptions in...