18 and 25 Feb 2004
CS 3243 - Logical Agents
32
Validity and satisfiability
nA sentence is valid if it is true in all models,
ne.g., True, A ÚØA, A Þ A, (A Ù (A Þ B)) Þ B
n
nValidity is connected to inference via the Deduction Theorem:
nKB ╞ α if and only if (KB Þ α) is valid
n
nA sentence is satisfiable if it is true in some model
ne.g., AÚ B, C
n
nA sentence is unsatisfiable if it is true in no models
ne.g., AÙØA
n
nSatisfiability is connected to inference via the following:
nKB ╞ α if and only if (KB ÙØα) is unsatisfiable