Results 1 
6 of
6
Constructing Conditional Plans by a TheoremProver
 Journal of Artificial Intelligence Research
, 1999
"... The research on conditional planning rejects the assumptions that there is no uncertainty or incompleteness of knowledge with respect to the state and changes of the system the plans operate on. Without these assumptions the sequences of operations that achieve the goals depend on the initial sta ..."
Abstract

Cited by 142 (6 self)
 Add to MetaCart
The research on conditional planning rejects the assumptions that there is no uncertainty or incompleteness of knowledge with respect to the state and changes of the system the plans operate on. Without these assumptions the sequences of operations that achieve the goals depend on the initial state and the outcomes of nondeterministic changes in the system. This setting raises the questions of how to represent the plans and how to perform plan search. The answers are quite different from those in the simpler classical framework. In this paper, we approach conditional planning from a new viewpoint that is motivated by the use of satisfiability algorithms in classical planning. Translating conditional planning to formulae in the propositional logic is not feasible because of inherent computational limitations. Instead, we translate conditional planning to quantified Boolean formulae. We discuss three formalizations of conditional planning as quantified Boolean formulae, and pr...
Optimized Encodings of Fragments of Type Theory in First Order Logic
 JLC: Journal of Logic and Computation
, 1994
"... The paper presents sound and complete translations of several fragments of MartinLof's monomorphic type theory to first order predicate calculus. The translations are optimised for the purpose of automated theorem proving in the mentioned fragments. The implementation of the theorem prover Gand ..."
Abstract

Cited by 7 (4 self)
 Add to MetaCart
The paper presents sound and complete translations of several fragments of MartinLof's monomorphic type theory to first order predicate calculus. The translations are optimised for the purpose of automated theorem proving in the mentioned fragments. The implementation of the theorem prover Gandalf and several experimental results are described. 1 Introduction The subject of this paper is the problem of automated theorem proving in MartinLof's monomorphic type theory [19, 8], which is the underlying logic of the interactive proof development system ALF [2, 14]. In the scope of our paper the task of automated theorem proving in type theory is understood as demonstrating that a certain type is inhabited by constructing a term of that type. The problem of inhabitedness of a type A is understood in the following way: given a set of judgements \Gamma (these may be constant declarations, explicit definitions and defining equalities), find a term a such that a2A is derivable from \Gam...
Completeness of Resolution for Definite Answers Tanel Tammet
 Journal of Logic and Computation
, 1995
"... We investigate the problem of finding a computable witness for the existential quantifier in a formula of the classical firstorder predicate logic. The Aresolution calculus based on the program derivation algorithm A of CL. Chang, R. CT. Lee and R.Waldinger is used for finding a definite substit ..."
Abstract
 Add to MetaCart
We investigate the problem of finding a computable witness for the existential quantifier in a formula of the classical firstorder predicate logic. The Aresolution calculus based on the program derivation algorithm A of CL. Chang, R. CT. Lee and R.Waldinger is used for finding a definite substitution t for an existentially bound variable y in some formula F , such that Fft=yg is provable. The term t is built of the function and predicate symbols in F , plus Boolean functions and a case splitting function if , defined in the standard way: if (True; x; y) = x and if (False; x; y) = y. We prove that the Aresolution calculus is complete in the following sense: if such a definite substitution exists, then the Acalculus derives a clause giving such a substitution. The result is strengthened by allowing the usage of liftable criterias R of a certain type, prohibiting the derivation of the substitution terms t for which R(t) fails. This enables us to specify, for example, that the subs...
Completeness of Resolution for Definite Answers Tanel Tammet
 Journal of Logic and Computation
, 1995
"... We investigate the problem of finding a computable witness for the existential quantifier in a formula of the classical firstorder predicate logic. The Aresolution calculus based on the program derivation algorithm A of CL. Chang, R. CT. Lee and R.Waldinger is used for finding a definite subs ..."
Abstract
 Add to MetaCart
We investigate the problem of finding a computable witness for the existential quantifier in a formula of the classical firstorder predicate logic. The Aresolution calculus based on the program derivation algorithm A of CL. Chang, R. CT. Lee and R.Waldinger is used for finding a definite substitution t for an existentially bound variable y in some formula F , such that Fft=yg is provable. The term t is built of the function and predicate symbols in F , plus Boolean functions and a case splitting function if , defined in the standard way: if (True; x; y) = x and if (False; x; y) = y. We prove that the Aresolution calculus is complete in the following sense: if such a definite substitution exists, then the Acalculus derives a clause giving such a substitution. The result is strengthened by allowing the usage of liftable criterias R of a certain type, prohibiting the derivation of the substitution terms t for which R(t) fails. This enables us to specify, for example, tha...
Reasoning Defeasibly about Plans
"... This technical report describes the construction of an experimental planner that finds plans by reasoning about them defeasibly rather than by running a search algorithm. The need for such a planner is defended in the paper "The Logical Foundations of GoalRegression Planning". 1. Planning Agents P ..."
Abstract
 Add to MetaCart
This technical report describes the construction of an experimental planner that finds plans by reasoning about them defeasibly rather than by running a search algorithm. The need for such a planner is defended in the paper "The Logical Foundations of GoalRegression Planning". 1. Planning Agents Practical applications of AI planning theory have only occurred in narrowly circumscribed domains in wich the goals are fixed and all the relevant information can be precompiled and supplied to the planner. The planner then runs a program that searches the space of possible plans (relative to the given information) until it finds a plan whose execution is guaranteed to achieve the goals. In such "applied planning", a planner is a tool used by a human being, and in order to use the tool effectively the human must prepare the ground very carefully, being sure to give the planner all the knowledge needed to solve the planning problem. Contemporary AI planning theory is based upon algorithmic planners. Given a planning problem, an algorithmic planner runs a program that systematically searches the space of possible plans until it returns one that purports to solve the problem. The sense in which the planner is algorithmic is that it executes an effective computation, i.e., the set of pairs problem,solution that characterize the planner is recursively enumerable. One of the ideals to which AI aspires is the construction of autonomous rational agents capable of maneuvering through a complex, variable, and often uncooperative environment. A special case of this is the attempt to build a system modeling human rationality. Planning will be an essential ingredient in any such agent. However, the planning problem faced by such an agent contrasts in important ways with the kind of applie...