Basic properties of the equivalence

Studia Logica 41 (1):17 - 40 (1982)
<span class='Hi'></span> In this paper we investigate some basic semantic and syntactic conditions characterizing the equivalence connective.<span class='Hi'></span> In particular we define three basic classes of algebras:<span class='Hi'></span> the class of weak equivalential algebras,<span class='Hi'></span> the class of equivalential algebras and the class of regular equivalential algebras <span class='Hi'></span>(see <span class='Hi'></span>[12]<span class='Hi'></span>).Weak equivalential algebras can be used to study purely equivalential fragments of relevant logics and strict equivalential fragments of some modal logics <span class='Hi'></span>(for investigations of strict implicational fragments of modal logics see <span class='Hi'></span>[20]<span class='Hi'></span>).<span class='Hi'></span> Equivalential algebras are suitable to study purely equivalential fragment of BCI and BCK logic <span class='Hi'></span>(see <span class='Hi'></span>[21]<span class='Hi'></span>, p.<span class='Hi'></span> 316)<span class='Hi'></span>. A subclass of the class of regular equivalential algebras is suitable to study equivalential fragments of ukasiewicz logics.<span class='Hi'></span> Some subvarieties of the class of regular equivalential algebras provide natural semantics for equivalential fragments of the intuitionistic prepositional logic and various intermediate logics <span class='Hi'></span>(see <span class='Hi'></span>[13]<span class='Hi'></span>).
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DOI 10.1007/BF00373491
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Arthur N. Prior (1962). Formal Logic. Oxford, Clarendon Press.

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