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Single Idea 10894

[filed under theme 5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction ]

Full Idea

A propositional logic set of sentences Γ is 'satisfiable' if there is at least one admissible truth-assignment that makes all of its sentences true.

Gist of Idea

A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true

Source

José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4)

Book Ref

Zalabardo,José L.: 'Introduction to the Theory of Logic' [Westview 2000], p.53

The 18 ideas from 'Introduction to the Theory of Logic'

10886 Determinacy: an object is either in a set, or it isn't [Zalabardo]
10887 Specification: Determinate totals of objects always make a set [Zalabardo]
10888 Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo]
10889 The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo]
10890 A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo]
10891 If a set is defined by induction, then proof by induction can be applied to it [Zalabardo]
10893 Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo]
10895 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo]
10892 We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo]
10894 A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo]
10896 Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo]
10897 A first-order 'sentence' is a formula with no free variables [Zalabardo]
10898 The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo]
10900 Logically true sentences are true in all structures [Zalabardo]
10901 Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo]
10899 Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo]
10903 A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo]
10902 We can do semantics by looking at given propositions, or by building new ones [Zalabardo]