The Relational Syllogistic in the Quantified Argument Calculus

We investigate the relational syllogistic as a fragment of the Quantified Argument Calculus (Quarc). The language contains polyadic predicates (together with their reordered forms) and singular terms. A truth-valuational semantics is provided for the fragment. A sound and complete tableau calculus is formulated, which is the first time semantic tableau is used in the study of Quarc. With certain techniques for analyzing and transforming tableaux, we prove that the satisfiability problem is decidable and is NLogSpace -complete with or without reordered predicates. Besides, when singular arguments are absent, the logic also admits a proof system consisting of syllogistic rules.