Computational Logic
Lecture 4
Propositional Resolution
Michael Genesereth
Autumn 2009
Axiom Schema Instances
( )
p (p p)
p (q p)
p (r p )
q (p q)
q (q q)
q (r q )
r (p r)
r (q r)
r (r r )
p (p p p )
p (p q p )
p (p r p)
p (p p p )
p (p q p )
p (p r p )
.
Computational Logic
Lecture 6
Relational Logic Semantics
Michael Genesereth
Autumn 2010
Propositional Logic Semantics
A Propositional logic interpretation is an association
between the propositional constants in a propositional
language and the truth valu
Computational Logic
Lecture 3
Logical Entailment
Michael Genesereth
Autumn 2010
Logical Reasoning
Logical Reasoning relates premises and co ncl usi on
does not say w het her co nclusion is true in general
says co ncl usi on true when ever premises are tru
Computational Logic
Lecture 2
Propositional Logic
Michael Genesereth
Autumn 2009
Complexity
The cherry blossoms in the spring sank.
9/23/10
2
1
Ambiguity
Leland Stanford Junior University
Leland-Stanford
Junior-University?
Leland-Stanford-Junior
Universit
Computational Logic
Lecture 7
Relational Proofs
Michael Genesereth
Autumn 2010
Logical Entailment
A set of premises logically entails a conclusion
( |= ) if and only if every interpretation that
satisfies also satisfies .
2
1
Propositional Interpretation
Computational Logic
Lecture 9
Resolution Preliminaries
Michael Genesereth
Autumn 2010
Resolution Principle
The Resolution Principle is a rule of inference.
Using the Resolution Principle alone (without axiom
schemata or other rules of inference), it is po
Computational Logic
Lecture 8
Properties of Relational Logic
Michael Genesereth
Autumn 2010
Structures
We can view an interpretation as vector consisting of
a universe of discourse and values for the items in the
signature of the language (when the signat