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NUMERICAL QUANTIFIERS AND THEIR USE IN REASONING WITH NEGATIVE INFORMATION

IP.com Disclosure Number: IPCOM000128596D
Original Publication Date: 1978-Dec-31
Included in the Prior Art Database: 2005-Sep-16
Document File: 9 page(s) / 30K

Publishing Venue

Software Patent Institute

Related People

Stuart C. Shapiro: AUTHOR [+3]

Abstract

Numerical quantifiers provide simple means of formalizing such statements as, "at least three people are in that room", "at most fifteen people are in the elevator", and "everybody has exactly two parents". Although numerical quantifiers generalize the existential quantifier, they have different uses in reasoning. The existential quantifier is most useful for supplying referents for designating phrases with no previously explicitly mentioned referent. Numerical quantifiers are most useful for reasoning by the process of elimination. Numerical quantifiers would, therefore, be a useful addition to the operators of a reasoning program or deductive question-answering system. They have been added to SNePS, the semantic Network Processing System, to further enhance its inference capabilities, This material is based on work supported in part by a Faculty Research Fellowship from the Research Foundation of State University of New'York, and in part by the National Science Foundation under Grant No. MCS78-02274.

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THIS DOCUMENT IS AN APPROXIMATE REPRESENTATION OF THE ORIGINAL.

NUMERICAL QUANTIFIERS AND THEIR USE IN REASONING WITH NEGATIVE INFORMATION*

Stuart C. Shapiro

February, 1979

Technical Report Number 153

This material is based on work supported in part by a Faculty Research Fellowship from the Research Foundation of State University of New York, and in part by the National Science Foundation under Grant No. MCS78-02274.

Key words: Reasoning; logic based reasoning; quantifiers; numerical quantifiers; negative information; negation; representation of knowledge; formal representations; semantic networks.

Abstract

Numerical quantifiers provide simple means of formalizing such statements as, "at least three people are in that room", "at most fifteen people are in the elevator", and "everybody has exactly two parents". Although numerical quantifiers generalize the existential quantifier, they have different uses in reasoning. The existential quantifier is most useful for supplying referents for designating phrases with no previously explicitly mentioned referent. Numerical quantifiers are most useful for reasoning by the process of elimination. Numerical quantifiers would, therefore, be a useful addition to the operators of a reasoning program or deductive question-answering system. They have been added to SNePS, the semantic Network Processing System, to further enhance its inference capabilities,

This material is based on work supported in part by a Faculty Research Fellowship from the Research Foundation of State University of New'York, and in part by the National Science Foundation under Grant No. MCS78-02274.

Introduction

Logic based reasoning programs, that is reasoning pro-grams based on operators (connectives, quantifiers, modals) which have been studied as part of formal logical systems benefit from the fact that the inferential properties of their operators are clear and well known. They need not be restricted, however, to a minimal set of operators. minimal sets of operators are useful for proving properties of logical systems such as consistency and completeness, but using a logical system for carrying out inferences is simplified (for people) by enlarging the set of basic operators. This is one reason that natural deduction systems like those of [Fitch, 19521, [Prawitz,, 1965) and [Weyhrauch, 19771, with reasonable sets of connectives and two rules of inference for each one, are easier to use than axiomatic systems with minimal sets of connectives, rules and axioms.

This pape r is motivated by an interest in programs that represent knowledge, including the knowledge of rules of reasoning, and that use those rules to perform reasoning. I believe that

State University of New York at Buffalo Page 1 Dec 31, 1978

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NUMERICAL QUANTIFIERS AND THEIR USE IN REASONING WITH NEGATIVE INFORMATION

such programs are enhanced by the availability of a large set of operators that typify and formally model as many of the modes of human...