In this paper, some implicational fragments of trivalent ?ukasiewicz logic are studied and the propositional first-order presented. The maximal consistent theories as Monteiro’s deductive systems Lindenbaum-Tarski algebra in both cases. Consequently, adequacy theorems with respect to suitable algebraic structures proven.

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...

A rooted circuit is firstly introduced for convex geometries (antimatroids). We generalize it for closure systems or equivalently for closure operators. A rooted circuit is a specific type of a pair (X, e) of a subset X, called a stem, and an element e 6∈ X, called a root. We introduce a notion called a ‘prime stem,’ which plays the key role in this article. Every prime stem is shown to be a ps...

Reducing the distance between informal and formal proofs in interactive theorem proving is a long-standing matter. An approach to this general topic is to increase automation in theorem provers: indeed, automation turns many small formal steps into one big step. In spite of the usual automation methods, there are still many situations where the user has to provide some information manually, whe...

1 Implicational completeness-a neglected topic Every serious computer scientist and logician knows that resolution is complete for rst-order clause logic. By this, of course, one means that the empty clause (representing contradiction) is derivable by resolution from every unsatissable set of clauses S. However, there is another { less well known { concept of completeness for clause logic, that...