Tableau-Based Model Generation for Relational Syllogistic Logics

I present an analytic tableau system for a small fragment of natural language called RC. RC is an extension of the classical Aristotelian syllogisms (“All computer-scientists are mathematicians”) to include relations in the form of transitive verbs (“All who hate all logic programmers know some who hate all proof theoreticians”) and to permit the negation of nouns (“Some non-linguists love all set-theorists.”) This logic is big enough to be interesting, but it’s small enough that we can actually get some results. In this case, the results are that my tableau system (with an appropriate growth strategy) can be used to generate finite models for any satisfiable set of formulas from RC in a finite amount of time. And if a set is unsatisfiable, then the strategy will, in finite time, result in a closed tableau, proving its unsatisfiability. I also discuss RC-tabModG, an implementation of the tableau system in MiniKanren (a relational programming system embedded in Scheme).