‎gautama and almost gautama algebras and their associated logics

Recently, gautama algebras were dened and investigated as a common generalization of the varietyrdblst of regular double stone algebras and the variety rklst of regular kleene stone algebras, both of whichare, in turn, generalizations of boolean algebras. those algebras were named in honor and memory of the twofounders of indian logic{akshapada gautama and medhatithi gautama. the purpose of this paper is todene and investigate a generalization of gautama algebras, called almost gautama algebras (ag, for short).more precisely, we give an explicit description of subdirectly irreducible almost gautama algebras. as consequences,explicit description of the lattice of subvarieties of ag and the equational bases for all its subvarieties are given. it isalso shown that the variety ag is a discriminator variety. next, we consider logicizing ag; but the variety ag lacksan implication operation. we, therefore, introduce another variety of algebras called almost gautama heytingalgebras (agh, for short) and show that the variety agh is term-equivalent to that of ag. next, a propositionallogic, called ag (or agh), is dened and shown to be algebraizable (in the sense of blok and pigozzi) with thevariety ag, via agh; as its equivalent algebraic semantics (up to term equivalence). all axiomatic extensions of thelogic ag, corresponding to all the subvarieties of ag are given. they include the axiomatic extensions rdblst,rklst and g of the logic ag corresponding to the varieties rdblst, rklst, and g (of gautama algebras),respectively. it is also deduced that none of the axiomatic extensions of ag has the disjunction property. finally,we revisit the classical logic with strong negation cn and classical nelson algebras cn introduced by vakarelov in1977 and improve his results by showing that cn is algebraizable with cn as its algebraic semantics and that thelogics rklst, rklsth, 3-valued lukasivicz logic and the classical logic with strong negation are all equivalent.