In this paper, reasoning with ambiguous representations is explored in a formal way, with ambiguities at the level of propositions in propositional logic and predicate logic, and ambiguous representations of scopings in predicate logic as the main examples. First a version of propositional logic with propositional ambiguities is presented and a sequent axiomatization for it is given. This is then extended to predicate logic. Next, predicate logic with scope ambiguities is introduced and discussed, and again a sequent calculus for it is proposed. The conclusion connects the results to natural language semantics, and briefly compares them with existing logics of ambiguity. An appendix gives completeness proofs for our versions of ambiguous propositional and predicate logic.

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Department of Computer Science [CS]

van Eijck, D.J.N, & Jaspars, J.O.M. (1996). Ambiguity and reasoning. Department of Computer Science [CS]. CWI.