Classics (Collection 2)


Using Rewriting Rules for Connection Graphs to Prove Theorems

Classics (Collection 2)

Choose a clause in the connection graph as a start clause.. Every literal in the start clause will be labeled as a goal literal. For every goal literal L and every clause C in the graph, if there is an edge E connecting literal L and a literal L' of clause C, change edge E to a directed edge by pointing from literal L' to literal L. Label all the remaining literals in C as goal literals. If we choose the clause consisting of literals 9 and 8 as a start clause, we obtain a directed connection graph shown in Figure 1. However, if we choose the clause consisting of literals 1 and 2 as a start clause, we obtain a directed connection graph shown in Figure 1.


Using Rewriting Rules for Connection Graphs to Prove Theorems

Classics (Collection 2)

Choose a clause in the connection graph as a start clause.. Every literal in the start clause will be labeled as a goal literal. For every goal literal L and every clause C in the graph, if there is an edge E connecting literal L and a literal L' of clause C, change edge E to a directed edge by pointing from literal L' to literal L. Label all the remaining literals in C as goal literals. If we choose the clause consisting of literals 9 and 8 as a start clause, we obtain a directed connection graph shown in Figure 1. However, if we choose the clause consisting of literals 1 and 2 as a start clause, we obtain a directed connection graph shown in Figure 1.


30 / Search And Search Representations

Classics (Collection 2)

We assume a system that contains the following components: a) A Lexical Retrieval component that can find the k best matching words in any region of an utterance subject to certain constraints and can be recalled to continue enumerating word matches in decreasing order of goodness (where possible constraints include anchoring the left or right end of the word to particular points in the utterance or to particular adjacent word matches). Each continuation event is assigned a priority score that can be guaranteed to bound the priority score of any word that can be generated by that event (e.g., derived from the score of the last word enumerated prior to the continuation). This consists of (i) creating the corresponding theory (a one-word theory in the case of a seed event), (ii) calling the Linguistic component to check the consistency of the theory and to make predictions for words and/or word classes that can occur adjacent to it, at each end of the theory, (iii) calling the Lexical Retrieval component to enumerate the k best matching words satisfying these predictions at each end of the theory, and (iv) generating a "word" event for each such word found. Assumptions The shortfall method assumes that the quality scores assigned to word matches by the Lexical Retrieval component are additive, so that theories are appropriately assigned scores that are the sums of the scores of the word matches contained in them (scores that are basically multiplicative can be handled by using their logarithms).


30 / Search And Search Representations

Classics (Collection 2)

We assume a system that contains the following components: a) A Lexical Retrieval component that can find the k best matching words in any region of an utterance subject to certain constraints and can be recalled to continue enumerating word matches in decreasing order of goodness (where possible constraints include anchoring the left or right end of the word to particular points in the utterance or to particular adjacent word matches). Each continuation event is assigned a priority score that can be guaranteed to bound the priority score of any word that can be generated by that event (e.g., derived from the score of the last word enumerated prior to the continuation). This consists of (i) creating the corresponding theory (a one-word theory in the case of a seed event), (ii) calling the Linguistic component to check the consistency of the theory and to make predictions for words and/or word classes that can occur adjacent to it, at each end of the theory, (iii) calling the Lexical Retrieval component to enumerate the k best matching words satisfying these predictions at each end of the theory, and (iv) generating a "word" event for each such word found. Assumptions The shortfall method assumes that the quality scores assigned to word matches by the Lexical Retrieval component are additive, so that theories are appropriately assigned scores that are the sums of the scores of the word matches contained in them (scores that are basically multiplicative can be handled by using their logarithms).


Using Patterns and Plans in Chess

Classics (Collection 2)

PARADISE (PArtern Recognition Applied to Directing SEarch), which finds the best move in tactically sharp middle game positions from the games of chess masters. The actions of the rules post concepts in the data base while the conditions match patterns in the chess position and data base. Chess has been one of the most popular domains for Al research, yet brute force searching programs with little chess knowledge play better chess than programs with more chess knowledge. The purpose of this research is to investigate the issues involved in expressing and using pattern-oriented knowledge to analyze a position, to provide direction for the search, and to communicate useful results from the search.


Using Patterns and Plans in Chess

Classics (Collection 2)

PARADISE (PArtern Recognition Applied to Directing SEarch), which finds the best move in tactically sharp middle game positions from the games of chess masters. The actions of the rules post concepts in the data base while the conditions match patterns in the chess position and data base. Chess has been one of the most popular domains for Al research, yet brute force searching programs with little chess knowledge play better chess than programs with more chess knowledge. The purpose of this research is to investigate the issues involved in expressing and using pattern-oriented knowledge to analyze a position, to provide direction for the search, and to communicate useful results from the search.


Prolegomena to a Theory of Mechanized Formal Reasoning

Classics (Collection 2)

Below, I outline the mechanizable analogues of the usual notions of model, interpretation, satisfaction, theory, and reflection principle. The three statements above are represented as MAN (Socrates) Vx. (MAN(x) MORTAL(x)) MORTAL(Socrates) Our goal is to prove (MAN(Socrates) A Vx. Consider the first order language L, and a model M. L (P,F,C) M (D,P,F,C) As usual, L is determined by a collection, P. of predicate symbols, a collection, F, of function symbols, and a collection, C, of constant symbols (Kleene (1952, pp.


Prolegomena to a Theory of Mechanized Formal Reasoning

Classics (Collection 2)

Below, I outline the mechanizable analogues of the usual notions of model, interpretation, satisfaction, theory, and reflection principle. The three statements above are represented as MAN (Socrates) Vx. (MAN(x) MORTAL(x)) MORTAL(Socrates) Our goal is to prove (MAN(Socrates) A Vx. Consider the first order language L, and a model M. L (P,F,C) M (D,P,F,C) As usual, L is determined by a collection, P. of predicate symbols, a collection, F, of function symbols, and a collection, C, of constant symbols (Kleene (1952, pp.


Achieving Several Goals Simultaneously

Classics (Collection 2)

In the synthesis of a plan or computer program, the problem of achieving several goals simultaneously presents special difficulties, since a plan to achieve one goal may interfere with attaining the others. This paper develops the following strategy: to achieve two goals simultaneously, develop a plan to achieve one of them and then modify that plan to achieve the second as well. THE REPRESENTATION OF ACTIONS AND SITUATIONS IN CONTEMPORARY PROBLEM SOLVING 2.1 The classical problem solvers 2.2 Regression and STRIPS operators 2.3 The use of contexts to represent a changing world 2.4 Influential actions 2.5 Escaping from the STRIPS assumption 2.6 The use of contexts to implement skeleton models 2.7 Hypothetical worlds 2.8 Complexity 2.9 Recapitulation ACKNOWLEDGMENTS REFERENCES My feet want to dance in the sun My head wants to rest in the shade The Lord says "Go out and have fun!" The present paper elaborates on the description of the method, reports on its implementation, discusses its application to general planning and robot problem solving, and points out some of its shortcomings and some projected improvements.


Achieving Several Goals Simultaneously

Classics (Collection 2)

In the synthesis of a plan or computer program, the problem of achieving several goals simultaneously presents special difficulties, since a plan to achieve one goal may interfere with attaining the others. This paper develops the following strategy: to achieve two goals simultaneously, develop a plan to achieve one of them and then modify that plan to achieve the second as well. THE REPRESENTATION OF ACTIONS AND SITUATIONS IN CONTEMPORARY PROBLEM SOLVING 2.1 The classical problem solvers 2.2 Regression and STRIPS operators 2.3 The use of contexts to represent a changing world 2.4 Influential actions 2.5 Escaping from the STRIPS assumption 2.6 The use of contexts to implement skeleton models 2.7 Hypothetical worlds 2.8 Complexity 2.9 Recapitulation ACKNOWLEDGMENTS REFERENCES My feet want to dance in the sun My head wants to rest in the shade The Lord says "Go out and have fun!" The present paper elaborates on the description of the method, reports on its implementation, discusses its application to general planning and robot problem solving, and points out some of its shortcomings and some projected improvements.