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Commonsense Reasoning, 2nd Edition
book

Commonsense Reasoning, 2nd Edition

by Erik T. Mueller
November 2014
Intermediate to advanced
516 pages
16h 34m
English
Morgan Kaufmann
Content preview from Commonsense Reasoning, 2nd Edition
Appendix A

Logical Foundations

Abstract We discuss the logical foundations of the event calculus: relations, inductive definitions, first-order logic, many-sorted first-order logic, second-order logic, real numbers, lists, and circumscription.

Keywords Relations, Inductive definitions, First-order logic, Many-sorted first-order logic, Second-order logic, Circumscription

A.1 Relations

Relations are used in the definitions of the semantics of first-order logic and many-sorted first-order logic, and in the section on state constraints (Section 3.4).

Definition A.1

An n-ary relation R on a set S is a subset of Sn.

Definition A.2

A binary relation R on a set S is a subset of S × S.

Definition A.4

A binary relation R ⊆ S × S is reflexive if and ...

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Publisher Resources

ISBN: 9780128014165