it has been encountering with large modifications and developments during recent decades and it makes large developments at rey & islamshahr regions. as the habitation areas as shaped in different dimensions. thought it can investigate the implicational structural at large scales even at littler scales too. nevertheless the essential applications of living areas on over coming life need such ha...

The present study is a sequel to [3] and [5]. We further explore preservational properties of a class of implicational connectives. The implicational approach to preservation examines what happens when the implicational connective is required to preserve various properties. We focus on a particular class of properties, called meta-valuational properties, and the class of implicational connectiv...

Shortest possible axiomatizations for the implicational fragments of the modal logics S4 and S5 are reported. Among these axiomatizations is included a shortest single axiom for implicational S4—which to our knowledge is the first reported single axiom for that system—and several new shortest single axioms for implicational S5. A variety of automated reasoning strategies were essential to our d...

We describe a method for obtaining classical logic from intuitionistic logic which does not depend on any proof system, and show that by applying it to the most important implicational relevance logics we get relevance logics with nice semantical and proof-theoretical properties. Semantically all these logics are sound and strongly complete relative to classes of structures in which all element...

For a ∧-semidistributive lattice L, we study some particular implicational systems and show that the cardinality of a minimum implicational basis is polynomial in the size of join-irreducible elements of the lattice L. We also provide a polynomial time algorithm to compute a minimum implicational basis for L. © 2006 Published by Elsevier B.V.

We study implicational formulas in the context of proof complexity of intuitionistic propositional logic (IPC). On the one hand, we give an efficient transformation of tautologies to implicational tautologies that preserves the lengths of intuitionistic extended Frege (EF ) or substitution Frege (SF ) proofs up to a polynomial. On the other hand, EF proofs in the implicational fragment of IPC p...

Heusch introduced the notion of pure implicational formulas. He showed that the falsiiability problem for pure implicational formulas with k negations is solvable in time O(n k). Such falsiiability results are easily transformed to satissability results on CNF formulas. We show that the falsiiability problem for pure implicational formulas is solvable in time O(k k n 2), which is polynomial for...