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E-raamat: The Logic of Knowledge Bases

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The Logic of Knowledge BasesSuurem pilt
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The idea of knowledge bases lies at the heart of symbolic, or "traditional," artificial intelligence. A knowledge-based system decides how to act by running formal reasoning procedures over a body of explicitly represented knowledge--a knowledge base. The system is not programmed for specific tasks; rather, it is told what it needs to know and expected to infer the rest.This book is about the logic of such knowledge bases. It describes in detail the relationship between symbolic representations of knowledge and abstract states of knowledge, exploring along the way the foundations of knowledge, knowledge bases, knowledge-based systems, and knowledge representation and reasoning. Assuming some familiarity with first-order predicate logic, the book offers a new mathematical model of knowledge that is general and expressive yet more workable in practice than previous models. The book presents a style of semantic argument and formal analysis that would be cumbersome or completely impractical with other approaches. It also shows how to treat a knowledge base as an abstract data type, completely specified in an abstract way by the knowledge-level operations defined over it.



This book describes in detail the relationship between symbolic representations of knowledge and abstract states of knowledge, exploring along the way the foundations of knowledge, knowledge bases, knowledge-based systems, and knowledge representation and reasoning.
Preface xv
Acknowledgements xvii
PART I
Introduction
3(16)
Knowledge
3(3)
Propositions
3(1)
Belief
4(1)
Representation
5(1)
Reasoning
6(1)
Why Knowledge representation and reasoning?
6(5)
Knowledge-based systems
7(1)
Why knowledge representation?
8(2)
Why reasoning?
10(1)
Knowledge representation systems
11(3)
The Knowledge and symbol levels
12(1)
A functional view: Tell and Ask
13(1)
The interaction language
13(1)
The rest of the book
14(2)
Bibliographic notes
16(1)
Exercises
17(2)
A First-Order Logical Language
19(24)
Why first-order logic?
19(2)
Why standard names?
21(2)
The syntax of the language L
23(2)
Domain of Quantification
25(1)
World state
26(1)
Term and formula semantic evaluation
27(1)
Satisfiability, implication and validity
28(1)
Properties of logic L
29(5)
Why a proof theory for L?
34(1)
Universal generalization
35(1)
The proof theory
35(2)
Example derivation
37(2)
Bibliographic notes
39(1)
Exercises
40(3)
An Epistemic Logical Language
43(14)
Why not just use L?
43(1)
Known vs. potential instances
44(1)
Three approaches to incomplete knowledge
44(2)
The Language KL
46(2)
Possible worlds
48(1)
Objective knowledge in possible worlds
49(2)
Meta-knowledge and some simplifications
51(3)
The semantics of KL
54(1)
Bibliographic notes
55(1)
Exercises
56(1)
Logical Properties of Knowledge
57(22)
Knowledge and truth
57(2)
Knowledge and validity
59(2)
Known individuals
61(3)
An axiom system for KL
64(3)
A Completencess proof
67(6)
Part 1
69(1)
Part 2
70(2)
Variant systems
72(1)
Reducibility
73(3)
Bibliographic notes
76(1)
Exercises
77(2)
The Tell and Ask Operations
79(18)
Overview
79(1)
The Ask operation
80(1)
The initial epistemic state: e0
81(1)
The monotonicity of knowledge
82(1)
The Tell operation
83(2)
Closed world assertions
85(3)
A detailed example
88(4)
Examples of Ask
88(2)
Examples of Tell
90(2)
Other operations
92(2)
Definitions
92(1)
Wh-questions
93(1)
Bibliographic notes
94(1)
Exercises
95(2)
Knowledge Bases as Representations of Epistemic States
97(14)
Equivalent epistemic states
97(2)
Representing knowledge symbolically
99(2)
Some epistemic states are not representable
101(1)
Representable states are sufficient
102(3)
Finite representations are not sufficient
105(2)
Representability and Tell
107(1)
Bibliographic notes
108(1)
Exercises
109(2)
The Representation Theorem
111(16)
The method
112(1)
Representing the known instances of a formula
113(4)
Reducing arbitrary sentences to objective terms
117(1)
Tell and Ask at the symbol level
118(1)
The example KB reconsidered
119(5)
Wh-questions at the symbol level
124(1)
Bibliographic notes
125(1)
Exercises
125(2)
Only-Knowing
127(16)
The logic of answers
127(2)
The language OL
129(1)
Some properties of OL
130(3)
Characterizing Ask and Tell
133(1)
Determinate sentences
134(4)
Bibliographic notes
138(2)
Exercises
140(3)
PART II
Only-Knowing and Autoepistemic Logic
143(20)
Examples of autoepistemic reasoning in OL
143(5)
Stable sets and stable expansions
148(1)
Relation to stable sets
149(2)
Relation to stable expansions
151(2)
Computing stable expansions
153(2)
Non-reducibility of OL
155(3)
Generalized stability
158(1)
Bibliographic notes
159(1)
Where do we go from here?
160(1)
Exercises
161(2)
On the Proof Theory of OL
163(16)
Knowing at least and at most
163(2)
Some example derivations
165(3)
Propositional completeness
168(5)
Incompleteness
173(3)
Bibliographic notes
176(1)
Where do we go from here?
176(1)
Exercises
176(3)
Only-Knowing-About
179(16)
The logic of only-knowing-about
179(7)
A formal semantics
180(1)
Some properties of only-knowing-about
181(4)
Prime implicates
185(1)
Ask and Tell
186(1)
Relevance
187(5)
Bibliographic notes
192(1)
Where do we go from here?
192(1)
Exercises
193(2)
Avoiding Logical Omniscience
195(28)
The Propositional case
197(7)
A proof theory
199(4)
Computing explicit belief
203(1)
The first-order case
204(16)
Some properties
208(3)
Deciding belief implication
211(9)
Bibliographic notes
220(1)
Where do we go from here?
220(1)
Exercises
221(2)
The logic EOL
223(22)
Semantics
223(4)
Equality
223(1)
Nested explicit belief
224(2)
Explicitly only-knowing
226(1)
Some properties of EOL
227(2)
Representing the explicity believed instances of a formula
229(2)
Reducing arbitrary sentences to objective terms
231(3)
Decidability results
234(3)
Ask and Tell
237(4)
Ask
237(1)
Tell
238(1)
Decidability
239(1)
Examples of Ask
239(2)
Bibliographic notes
241(1)
Where do we go from here?
241(1)
Exercises
242(3)
Knowledge and Action
245(28)
A theory of action
245(6)
Action preconditions
246(1)
Action sensing
247(1)
Action effects
248(1)
The frame problem and a solution
248(2)
Basic action theories
250(1)
The logic AOL
251(4)
Knowledge after action
255(4)
An informal characterization
256(1)
Knowing in AOL
257(2)
Only-knowing in AOL
259(1)
Using AOL
259(3)
An axiomatization of AOL
262(7)
Bibliographic notes
269(1)
Where do we go from here?
269(1)
Exercises
270(3)
Epilogue 273(2)
References 275(6)
Index 281


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