Download My own slides. - Computer Science

Introduction to AI
&
AI Principles (Semester 1)
WEEK 8 (07/08)
[Barnden’s slides only]
John Barnden
Professor of Artificial Intelligence
School of Computer Science
University of Birmingham, UK
Predicate Logic—The Meat
 Predicate logic itself just consists of special symbols such as:
 ()
and the syntax (grammar)—how to structure expressions …
and general rules about the semantics of expressions (their
meanings) …
and general procedures for doing deductive inference.
 The particular symbols for entities, properties and
relationships (e.g., TheodosiaKirkbride, happy, taller-than), and
their meanings,
are up to the particular representation-developer.
Truth Values in Logic
(Part of the Semantics)
 Each formula (i.e., expression that makes a statement) is
considered to be either TRUE (T) or FALSE (F).
 This is the formula's truth value (sometimes called its
valuation).
 Formulas with standard propositional structure (by
conjunction, disjunction, implication, negation and related
constructors) have their truth values determined rigorously by
the truth values of their subformulas.
Related principles handle generalization.
 There is no middle ground between TRUE and FALSE.
Clearly, this definiteness is a problem, in the case of many
types of statement.
Representing States at Different Times
 Standard logic has no inbuilt facility for changes of truth
value because of changes in the represented world.
 So, the formulas are either about matters that are unchanging
by their very nature (“eternal” matters):

91 is prime
(NB: this is an enternal falsehood)
or are implicitly about some particular “time-slice” of the
represented world:

Mary has three cars
or are explicitly about some particular time-slice:

On 22 Feb 2005 at 10am, Mary had three cars.
Changing One’s Mind
Equally, standard logic does not itself contain any
mechanism for a system changing its mind about
the truth of something,


e.g changing its mind about whether 91 is a prime number
or not,
or about whether Mary has three cars at 10am on 22 Feb
2005.
However, in an AI system, formulas can be made to
change in truth-value (either because of world
change or system changing its mind, or both), if
special, extra mechanisms are added.
Why Logic Has Been Proposed
Desire to capture human rationality.
Desire for general-purpose representation/reasoning
approach.

General purpose in terms of both subject matter and role in
cognition (info from vision, sentence meanings, internal memory,
…)
Desire for common format for explaining what is going
on in other representation/reasoning approaches.
Rationality
 Much concentration in history on people as (in part) rational beings.
 Rationality as involving sound reasoning (deduction)

i.e. reasoning where truth of outputs is guaranteed by truth of inputs.
 Analysis of deduction, leading to development of standard logics as
(supposedly) important descriptors of human thought.
 Spillover of the results, and some of the thinking behind it, into AI.
 Standard logic does not have inbuilt facilities for unsound
reasoning (involving uncertainty, assumptions, abduction,
induction, analogy, …) even though this is crucial in real life …
 It’s quite difficult to add such facilities, but there have been many
proposals.
“General-Purpose” Aim
 Reaction to: completely ad hoc, special-purpose
representations, and representation styles, created for specific
tasks, specific types of task or specific types of information.
Consequence of such special-purpose representations:



Duplication of representational design effort when approaching a new
problem.
Difficulty of learning transferrable lessons about representational
design.
Need for creating tailored reasoning methods to cope with the
specialized representations.
 A single AI system may need to deal with a wide variety of
tasks and types of information, perhaps all mixed up together.
Having disparate representation styles for different types of
information causes problems ... ... ...