. I present a new tableaux-based model generation method for first-order formulas without function symbols. Unlike comparable approaches, the Relational Models (RM) tableaux calculus does not require clausal input theories. I propose some applications of the RM calculus in natural-language semantics and discuss its usefulness as an inference procedure in natural-language processing. 1 Introduction Refutational methods in automated deduction prove the unsatisfiability of logical theories. For many applications, the interpretations of a theory that show its satisfiability are at least as interesting as proofs. Model generation refers to the automatic construction of such interpretations from first-order theories. In the recent years, there has been a growing interest in the automated deduction community in developing model generation methods for various application areas such as finite mathematics [25, 22], deductive databases [7], diagnosis [13, 1], and planning [19]. As a result, mode...

Finding countermodels is an effective way of disproving false conjectures. In first-order predicate logic, model finding is an undecidable problem. But if a finite model exists, it can be found by exhaustive search. The finite model generation problem in the first-order logic can also be translated to the satisfiability problem in the propositional logic. But a direct translation may not be very efficient. This paper discusses how to take the symmetries into account so as to make the resulting problem easier. A static method for adding constraints is presented, which can be thought of as an approximation of the least number heuristic (LNH). Also described is a dynamic method, which asks a model searcher like SEM to generate a set of partial models, and then gives each partial model to a propositional prover. The two methods are analyzed, and compared with each other.

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When logical inference helps determining textual entailment

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