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## ARTIFICIAL INTELLIGENCE [INTELLIGENT AGENTS PARADIGM]

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### Title: WHY WOULD YOU STUDY ARTIFICIAL INTELLIGENCE? (1) Author: MELNIS Last modified by: janis Created Date: 1/20/2002 11:33:39 AM Document presentation format – PowerPoint PPT presentation

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Title: ARTIFICIAL INTELLIGENCE [INTELLIGENT AGENTS PARADIGM]

1
ARTIFICIAL INTELLIGENCEINTELLIGENT AGENTS
INFERENCE RULES
• Professor Janis Grundspenkis
• Riga Technical University
• Faculty of Computer Science and Information
Technology
• Institute of Applied Computer Systems
• Department of Systems Theory and Design
• E-mail Janis.Grundspenkis_at_rtu.lv

2
Inference Rules
Modus Ponens or Implication Elimination
From two sentences ? ? ? and ? that are true (so
called axioms) the new true sentence ? can be
concluded (a theorem is proved with respect to
the axioms, i.e. the theorem logically follows
from the axioms).
3
Inference Rules
• Example
• Sentence If sun shines it is warm
• A sun shines B it is warm.
• Axioms A ? B
• A
• Theorem B, i.e., it is warm.

4
Inference Rules
AND-Elimination
From a conjunction of sentences any of conjuncts
can be inferred.
5
Inference Rules
AND-Introduction
From a list of sentences their conjunction can be
inferred.
6
Inference Rules
OR-Introduction
From a sentence its disjunction with anything
else at all can be inferred.
7
Inference Rules
Double-Negation Elimination
From a double negated sentence a positive
sentence can be inferred.
8
Inference Rules
Unit Resolution
From a disjunction, if one of the disjuncts is
false it can be inferred that the other one is
true.
9
Inference Rules
or equivalently
Since ? cannot be both true and false, one of the
other disjuncts must be true in one of the
premises. Or equivalently, implication is
transitive.
10
Inference Rules
Modus Tolens
? ? ?? ?? ???
T T F F T
T F F T F
F T T F T
F F T T T
or equivalently
11
Inference Rules
Abduction Rule
? ? ???
T T T
T F F
F T T
F F T
It is not a sound inference rule!
12
Inference Rules
PROOF THEORY AND PROCEDURE The proof theory is a
set of rules for logical inferencing the
entailments of a set of sentences. The way to
prove a theorem is to use a proof procedure. A
proof procedure is a combination of an inference
rule and an algorithm for applying that rule to a
set of logical expressions to generate new
sentences.
13
Inference Rules
PROOF PROCEDURE (continued) Proof procedures use
manipulations called sound rules of inference
that produce new expressions from old
expressions. More precisely, models of the old
expressions are guaranteed to be models of the
new ones too.
14
Inference Rules
PROOF PROCEDURE (continued) The most
straightforward proof procedure is to apply sound
rules of inference to the axioms, and to the
results of applying sound rules of inference,
until the desired theorem appears.
15
Inference Rules
PROOF PROCEDURE (continued) A logical proof
consists of a sequence of applications of
inference rules, starting with sentences
initially in the knowledge base, and ending with
the generation of the sentence whose proof is
desired. The job of an inference procedure is to
construct proof by finding appropriate sequences
of applications of inference rules.