LACL '98 Selected papers from the Third International Conference, on Logical Aspects of Computational Linguistics
A Resolution Calculus for Dynamic Semantics
JELIA '98 Proceedings of the European Workshop on Logics in Artificial Intelligence
A Tableaux Calculus for Ambiguous Quantification
TABLEAUX '98 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Bidirectional contextual resolution
Computational Linguistics
A survey of semantic description frameworks for programming languages
ACM SIGPLAN Notices
Scope Dominance with Monotone Quantifiers over Finite Domains
Journal of Logic, Language and Information
Scope Dominance with Generalized Quantifiers
Languages: From Formal to Natural
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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.