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Kowalski R. Logic for Problem Solving, Revisited 2014
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This seminal book of Computer Science is the most cited reference on the subject of programming in logic. Originally published in 1979, this now classic text was the first comprehensive attempt to define the scope of logic for problem solving. In this extended edition, Robert Kowalski revisits his classic text in the light of subsequent developments in a substantial commentary of fifty pages.
This work investigates the application of logic to problem-solving and computer programming. It assumes no previous knowledge of these fields, and may be appropriate therefore as an introduction to logic, the theory of problem-solving, and computer programming. At the focal point is Computational Logic. It centers around the famous slogan: Algorithm = Logic + Control, which was coined by the author and is explained in this book. According to this view, an algorithm consists of a problem description (the logic part) and a strategy to perform useful computations on this description (the control part). This separation of concerns ideally leads to declarative programs that are simple to develop, clear to understand and easy to maintain.
Prefaces to the 2014 Extended Edition
Preface to the 1979 Edition
Introduction
The family relationships example and clausal form
A more precise definition of clausal form
Top-down and bottom-up presentation of definitions
Semantics of clausal form
The fallible Greek example
The factorial example
The universe of discourse and interpretations
A more precise definition of inconsistency
The semantics of alternative conclusions
Horn clauses
Mushrooms and toadstools
Exercises
Representation in Clausal Form
Infix notation
Variables and types of individuals
Existence
Negation
Denial of conclusions which are implications
Conditions which are implications
Definitions and "if-and-only-if"
Semantic networks
Extended semantic networks
The representation of information by binary predicate symbols
Advantages of the binary representation
Databases
Data query languages
Data description
Integrity constraints
A departmental database
Equality
Exercises
Top-down and Bottom-up Horn Clause Proof Procedures
Introduction
The parsing problem
A predicate logic representation of the parsing problem
Bottom-up inference
Top-down inference
The family relationships example
Inference rules and search strategies
Infinite search spaces: natural numbers
Definitions
Substitution and matching
Correctness and completeness of inference systems
Exercises
Horn Clause Problem-Solving
Path-finding
The water containers problem
A simplified path-finding problem
Graph-representation of search spaces
The Search Spaces for the Water Containers Problem
Search strategies for path-finding
The and-or tree representation of problem-reduction
The problem-solving interpretation of Horn clauses
Splitting and independent subgoals
Dependent subgoals
Finding versus showing
Lemmas, duplicate subgoals and loops
Search strategies for problem-reduction spaces
Bi-directional problem-solving
A notation for describing bi-directional problem-solving
Another formulation of the path-finding problem
Other aspects of problem-solving
Exercises
The Procedural Interpretation of Horn Clauses
Terms as data structures
Computation by successive approximation to output
The variation of input-output parameters
Non-determinism 1: several procedures match a procedure call
Sequential search regarded as iteration
"Don’t know" versus "don’t care" non-determinism
Non-determinisn 2: The scheduling of procedure calls
Bottom-up execution of programs
The pragmatic content of logic programs
Separation of data structures
Terms versus relations as data structures
Database formalisms and programming languages
Algorithm = Logic + Control
Specification of the control component
Natural Language = Logic + Control
Exercises
Plan-Formation and the Frame Problem
Plan-formation and the blocks world
A clausal representation of the blocks world problem
Bottom-up execution of the state space axiom (12)
Bottom-up execution of the frame axiom (15)
Mixed top-down and bottom-up execution of the frame axiom
Top-down execution of the state space and frame axioms
Applications of plan-formation
Limitations
Exercises
Resolution
Negative goals and assertions
Resolution
Middle out reasoning with Horn clauses
Propositional logic example
Arrow notation for non-Horn clauses
Disjunctive solutions to non-Horn clause problems
Factoring
Exercises
The Connection Graph Proof Procedure
The initial connection graph
The Resolution of links in connection graphs
Mixed top-down and bottom-up search - the parsing problem
Macro-processing and middle-out reasoning
Arrow notation for controlling selection of links
Self-resolving clauses
Deletion of links whose resolvents are tautologies
The connection graph proof procedure
Exercises
Global Problem-Solving Strategies
Deletion of redundant subgoals
Addition of surrogate subgoals
Rejection of inconsistent goal statements
Generalising the use of diagrams in geometry
Goals as generalised solutions
Goal transformation and the information explosion
Loop detection by analysis of differences
The factorial example
Invariant properties of procedures
Exercises
Comparison of Clausal Form with Standard Form
Introduction to the standard form of logic
Conversion to clausal form
Comparison of clausal form with standard form
Conjunctive conclusions and disjunctive conditions
Disjunctive conclusions
Only-if halves of definitions
Implications as conditions of implications
Derivation of programs from specifications
Exercises
If-and-only-if
The need for the only-if halves of definitions
Terms versus relations as data structures
The unstated only-if-assumption
Ambiguity of only-if
Object language and meta-language solutions
Object language and meta-language interpretations of negation
Horn clauses augmented with negation interpreted as failure
Proof of program properties
The monotonicity criticism of logical consequence
Exercises
Formalisation of Provability
Correct representability
A simple definition of a provability relation
Direct execution versus simulation
Addition and suppression of assumptions
Bootstrapping
Combining the object language and meta-language
Incompleteness of the combined object and meta-language
More comprehensive form of the Demonstrate relation
Exercises
Logic, Change and Contradiction
Information systems
Dynamics of information system change
Restoration of consistency
A logic program for natural language
Conclusion
References
Index
Errata of the 1979 Edition Logic for Problem Solving, Revisited
Introduction
Representation in Clausal Form
Top-down and Bottom-up Horn Clause Proof Procedures
Horn Clause Problem-Solving
The Procedural Interpretation of Horn Clauses
Plan-Formation and the Frame Problem
Resolution
The Connection Graph Proof Procedure
Global Problem-Solving Strategies
Comparison of Clausal Form with Standard Form
If-and-only-if
Formalisation of Provability
Logic, Change and Contradiction
Acknowledgements
New References