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Ambiguity and Reasoning
, 1995
"... 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 wit ..."
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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. AMS Subject Classification (1991): 03B65, 03B80, 68S05, 68T30, 92K20. CR Subject Classification (1991): F.3.1, F.3.2, I.2.1, I.2.4, I.2.7. Keyword and Phrases: Semantics of Natural Language, Reasoning with Underspec...
Horn extended feature structures: Fast unification with negation and limited disjunction
 In Fifth Conference of the EACL
, 1991
"... The notion of a Horn extended feature structure (Hoxf) is introduced, which is a feature structure constrained so that its only allowable extensions are those satisfying some set of Horn clauses in featureterm logic. Hoxf’s greatly generalize ordinary feature structures in admitting explicit repres ..."
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The notion of a Horn extended feature structure (Hoxf) is introduced, which is a feature structure constrained so that its only allowable extensions are those satisfying some set of Horn clauses in featureterm logic. Hoxf’s greatly generalize ordinary feature structures in admitting explicit representation of negative and implicational constraints. In contradistinction to the general case in which arbitrary logical constraints are allowed (for which the best known algorithms are exponential), there is a highly tractable algorithm for the unification of Hoxf’s. † The research reported herein was performed while the author was visiting the COSMOS Computational
clauses and featurestructure logic: Principles and unification algorithms, LLI
, 1993
"... The desirability of Horn clauses in logical deductive systems has long been recognized. The reasons are at least threefold. Firstly, while inference algorithms for full logics of any reasonable extent are typically intractable, for systems restricted to Horn clauses the picture is much better. (For ..."
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The desirability of Horn clauses in logical deductive systems has long been recognized. The reasons are at least threefold. Firstly, while inference algorithms for full logics of any reasonable extent are typically intractable, for systems restricted to Horn clauses the picture is much better. (For example, in ordinary propositional logic, while the full satisfiability problem is NPcomplete, a lineartime algorithm exists for Horn clauses.) Secondly, the knowledgerepresentation capabilities of Horn clauses, while weaker than those of the full logic, remain remarkably rich; indeed, far richer than that of simple conjunctive logic alone. Thirdly, Horn clauses define the maximal subset of a full logic which has the property of admitting generic models, which roughly means that for any set of Horn clauses, there is a least model of the clauses in that set. It is the purpose of this paper to initiate an investigation of Horn clause logic for an extended class of feature structures. After laying the groundwork for this context, we provide two key results. In the first, we show how the property of admitting
Feature Structures
"... plex (the feature structures 2 and 3 ). If we take FSs to be sets of paths and values, we will characterize (1) by saying, e.g. that the value of the path head j agr j num is sing. If we take them as functions, we will say (where f 1 means the feature structure tagged 1 above, and (f 1 cat) means th ..."
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plex (the feature structures 2 and 3 ). If we take FSs to be sets of paths and values, we will characterize (1) by saying, e.g. that the value of the path head j agr j num is sing. If we take them as functions, we will say (where f 1 means the feature structure tagged 1 above, and (f 1 cat) means the application the function f 1 to the argument cat). (2) a. (f 1 cat) = s b. (f 2 agr) = (f 3 agr) c. (f 2 agr) = f 4 d. ((f 1 head) agr) = (f 2 agr) If we take them to be DAGs we will think of them as follows: 1 (3) 1 subj 2 cat np agr cat s head 3 agr 4 num sing per 3 cat vp Thinking