Logical Foundations
This appendix discusses 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.
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.3
A binary relation R ⊆ S × S is reflexive if and only if, for every a ∈ S, 〈a, a〉 ∈ R.
DEFINITION A.4
A binary relation R ⊆ S × S is irreflexive if and only if, for every ...
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