Knowledge Representation using Logic
The aim of this section is to show how logic can be used to form representations
of the world and how a process of inference can be used to derive new representations
about the world and how these can be used by an intelligent agent to deduce
what to do.
We require:
- A formal language to represent knowledge in
a computer tractable form.
- Reasoning -
Processes to manipulate this knowledge to deduce non-obvious facts.
Why logic?
The challenge is to design a language which allows one to represent
all the necessary knowledge.
We need to be able to make statements about the world such as
describing things - people, houses, theories etc;
relations between things and properties of things.
Logic makes statements about the world which are true (or false) if
the state of affairs it represents is the case (or not the case). Compared to
natural languages (expressive but context sensitive) and programming languages
(good for concrete data structures but not expressive) logic combines the advantages
of natural languages and formal languages. Logic is:
- concise
- unambiguous
- context insensitive
- expressive
- effective for inferences
A logic is defined by the following:
- Syntax - describes the possible configurations that
constitute sentences.
- Semantics - determines what facts in the world the sentences refer
to i.e. the interpretation.
Each sentence makes a claim about the world.
- Proof theory - set of rules for generating new
sentences that are necessarily true
given that the old sentences are true.
The relationship between sentences is called entailment.
The semantics link these sentences (representation) to facts of the world.
The proof can be used to determine new facts which follow from the old.
We will consider two kinds of logic:
propositional logic
and first-order logic or more precisely first-order
predicate calculus.
Propositional logic is of limited expressiveness but is useful to
introduce many of the concepts of logic's syntax, semantics and
inference procedures.
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