Equivalential Structures for Binary and Ternary Syllogistics

The aim of this paper is to provide a contribution to the natural logic program which explores logics in natural language. The paper offers two logics called $$ \mathcal {R}(\forall ,\exists ) $$R(∀,∃) and $$ \mathcal {G}(\forall ,\exists ) $$G(∀,∃) for dealing with inference involving simple sentences with transitive verbs and ditransitive verbs and quantified noun phrases in subject and object position. With this purpose, the relational logics (without Boolean connectives) are introduced and a model-theoretic proof of decidability for they are presented. In the present paper we develop algebraic semantics (bounded meet semi-lattice) of the logics using congruence theory.

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