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31
On the compilability and expressive power of propositional planning formalisms
, 1998
"... The recent approaches of extending the GRAPHPLAN algorithm to handle more expressive planning formalisms raise the question of what the formal meaning of “expressive power ” is. We formalize the intuition that expressive power is a measure of how concisely planning domains and plans can be expressed ..."
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Cited by 88 (10 self)
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The recent approaches of extending the GRAPHPLAN algorithm to handle more expressive planning formalisms raise the question of what the formal meaning of “expressive power ” is. We formalize the intuition that expressive power is a measure of how concisely planning domains and plans can be expressed in a particular formalism by introducing the notion of “compilation schemes ” between planning formalisms. Using this notion, we analyze the expressiveness of a large family of propositional planning formalisms, ranging from basic STRIPS to a formalism with conditional effects, partial state specifications, and propositional formulae in the preconditions. One of the results is that conditional effects cannot be compiled away if plan size should grow only linearly but can be compiled away if we allow for polynomial growth of the resulting plans. This result confirms that the recently proposed extensions to the GRAPHPLAN algorithm concerning conditional effects are optimal with respect to the “compilability ” framework. Another result is that general propositional formulae cannot be compiled into conditional effects if the plan size should be preserved linearly. This implies that allowing general propositional formulae in preconditions and effect conditions adds another level of difficulty in generating a plan.
Preprocessing of Intractable Problems
- Information and Computation
, 1997
"... Some computationally hard problems --e.g., deduction in logical knowledge bases-- are such that part of an instance is known well before the rest of it, and remains the same for several subsequent instances of the problem. In these cases, it is meaningful to preprocess off-line this known part so as ..."
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Cited by 45 (15 self)
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Some computationally hard problems --e.g., deduction in logical knowledge bases-- are such that part of an instance is known well before the rest of it, and remains the same for several subsequent instances of the problem. In these cases, it is meaningful to preprocess off-line this known part so as to simplify the remaining on-line problem. In this paper we investigate such a technique in the context of intractable, i.e., NP-hard, problems. Recent results in the literature show that not all NP-hard problems behave in the same way: for some of them preprocessing yields polynomial-time on-line simplified problems (we call them compilable), while for other ones there is strong evidence that this should not happen. Our primary goal is to provide a sound methodology that can be used either to prove or disprove that a problem is compilable. To this end, we define new models of computation, complexity classes, and reductions. We find complete problems for such classes, completeness meaning...
A Perspective on Knowledge Compilation
- In Proc. International Joint Conference on Artificial Intelligence (IJCAI
, 2001
"... We provide a perspective on knowledge compilation which calls for analyzing different compilation approaches according to two key dimensions: the succinctness of the target compilation language, and the class of queries and transformations that the language supports in polytime. We argue that ..."
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Cited by 31 (9 self)
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We provide a perspective on knowledge compilation which calls for analyzing different compilation approaches according to two key dimensions: the succinctness of the target compilation language, and the class of queries and transformations that the language supports in polytime. We argue that such analysis is necessary for placing new compilation approaches within the context of existing ones.
Semantic Forgetting in Answer Set Programming
, 2008
"... The notion of forgetting, also known as variable elimination, has been investigated extensively in the context of classical logic, but less so in (nonmonotonic) logic programming and nonmonotonic reasoning. The few approaches that exist are based on syntactic modifications of a program at hand. In t ..."
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Cited by 30 (11 self)
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The notion of forgetting, also known as variable elimination, has been investigated extensively in the context of classical logic, but less so in (nonmonotonic) logic programming and nonmonotonic reasoning. The few approaches that exist are based on syntactic modifications of a program at hand. In this paper, we establish a declarative theory of forgetting for disjunctive logic programs under answer set semantics that is fully based on semantic grounds. The suitability of this theory is justified by a number of desirable properties. In particular, one of our results shows that our notion of forgetting can be entirely captured by classical forgetting. We present several algorithms for computing a representation of the result of forgetting, and provide a characterization of the computational complexity of reasoning from a logic program under forgetting. As applications of our approach, we present a fairly general framework for resolving conflicts in inconsistent knowledge bases that are represented by disjunctive logic programs, and we show how the semantics of inheritance logic programs and update logic programs from the literature can be characterized through forgetting. The basic idea of the conflict resolution framework is to weaken the preferences of each agent by forgetting certain knowledge that causes inconsistency. In particular, we show how to use the notion of forgetting to provide an elegant solution for preference elicitation in disjunctive logic programming.
Representing utility functions via weighted goals. Mathematical Logic Quarterly
, 2009
"... Key words Preference representation, computational complexity, computational social choice. We analyze the expressivity, succinctness, and complexity of a family of languages based on weighted propositional formulas for the representation of utility functions. The central idea underlying this form o ..."
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Cited by 17 (11 self)
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Key words Preference representation, computational complexity, computational social choice. We analyze the expressivity, succinctness, and complexity of a family of languages based on weighted propositional formulas for the representation of utility functions. The central idea underlying this form of preference modeling is to associate numerical weights with goals specified in terms of propositional formulas, and to compute the utility value of an alternative as the sum of the weights of the goals it satisfies. We define a large number of representation languages based on this idea, each characterized by a set of restrictions on the syntax of formulas and the range of weights. Our aims are threefold. First, for each language we try to identify the class of utility functions it can express. Second, when different languages can express the same class of utility functions, one may allow for a more succinct representation than another. Therefore, we analyze the relative succinctness of languages. Third, for each language we study the computational complexity of the problem of finding the most preferred alternative given a utility function expressed in that language. c ○ 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1
From Preference Logics to Preference Languages, and Back
"... Preference logics and AI preference representation languages are both concerned with reasoning about preferences on combinatorial domains, yet so far these two streams of research have had little interaction. This paper contributes to the bridging of these areas. We start by constructing a “prototyp ..."
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Cited by 15 (2 self)
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Preference logics and AI preference representation languages are both concerned with reasoning about preferences on combinatorial domains, yet so far these two streams of research have had little interaction. This paper contributes to the bridging of these areas. We start by constructing a “prototypical” preference logic, which combines features of existing preference logics, and then we show that many well-known preference languages, such as CP-nets and its extensions, are natural fragments of it. After establishing useful characterizations of dominance and consistency in our logic, we study the complexity of satisfiability in the general case as well as for meaningful fragments, and we study the expressive power as well as the relative succinctness of some of these fragments. 1.
On Eliminating Disjunctions in Stable Logic Programming
- PROCEEDINGS OF THE 9TH INTERNATIONAL CONFERENCE ON PRINCIPLES OF KNOWLEDGE REPRESENTATION AND REASONING (KR 2004
, 2003
"... Disjunction is generally considered to add expressive power to logic programs under the stable model semantics, which have become a popular programming paradigm for knowledge representation and reasoning. However, disjunction is often not really needed, in that an equivalent program without disju ..."
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Cited by 13 (9 self)
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Disjunction is generally considered to add expressive power to logic programs under the stable model semantics, which have become a popular programming paradigm for knowledge representation and reasoning. However, disjunction is often not really needed, in that an equivalent program without disjunction can be given. In this paper, we consider the question, given a disjunctive logic program, P , under which conditions does there exist an equivalent normal (i.e., disjunction-free) logic program P . In fact, we study this problem under different notions of equivalence, viz. for ordinary equivalence (considering the collections of all stable models of the programs) as well as for the more restrictive notions of strong and uniform equivalence. We resolve the issue for propositional programs on which we focus here, and present a simple, appealing semantic criterion from which all disjunctions can be eliminated under strong equivalence; testing this criterion is coNP-complete, but the class of programs satisfying it has the same complexity as disjunctive logic programs in general. We also show that under ordinary and uniform equivalence, disjunctions can always be eliminated. In all cases, we give constructive methods to achieve this. However, we also provide evidence that disjunctive logic programs are a more succinct knowledge representation formalism than normal logic programs under all these notions of equivalence.
Forgetting and conflict resolving in disjunctive logic programming
- IN PROC. OF AAAI
, 2006
"... We establish a declarative theory of forgetting for disjunctive logic programs. The suitability of this theory is justified by a number of desirable properties. In particular, one of our results shows that our notion of forgetting is completely captured by the classical forgetting. A transformation- ..."
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Cited by 10 (5 self)
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We establish a declarative theory of forgetting for disjunctive logic programs. The suitability of this theory is justified by a number of desirable properties. In particular, one of our results shows that our notion of forgetting is completely captured by the classical forgetting. A transformation-based algorithm is also developed for computing the result of forgetting. We also provide an analysis of computational complexity. As an application of our approach, a fairly general framework for resolving conflicts in inconsistent knowledge bases represented by disjunctive logic programs is defined. The basic idea of our framework is to weaken the preferences of each agent by forgetting certain knowledge that causes inconsistency. In particular, we show how to use the notion of forgetting to provide an elegant solution for preference elicitation in disjunctive logic programming.
In Defense of PDDL Axioms
, 2005
"... There is controversy as to whether explicit support for PDDL-like axioms and derived predicates is needed for planners to handle real-world domains effectively. Many researchers have deplored the lack of precise semantics for such axioms, while others have argued that it might be best to compil ..."
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Cited by 5 (0 self)
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There is controversy as to whether explicit support for PDDL-like axioms and derived predicates is needed for planners to handle real-world domains effectively. Many researchers have deplored the lack of precise semantics for such axioms, while others have argued that it might be best to compile them away. We propose an adequate semantics for PDDL axioms and show that they are an essential feature by proving that it is impossible to compile them away if we restrict the growth of plans and domain descriptions to be polynomial. These results suggest that adding a reasonable implementation to handle axioms inside the planner is beneficial for the performance. Our experiments confirm this suggestion.
Compilability of Abduction
- Tech. Rep. cs.AI/0210007, Computing Research Repository (CoRR
, 2000
"... Abduction is one of the most important forms of reasoning and it has been successfully applied to several practical problems such as diagnosis. In this paper we investigate whether the computational complexity of abduction can be reduced by an appropriate use of preprocessing or compilation. Thi ..."
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Cited by 3 (0 self)
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Abduction is one of the most important forms of reasoning and it has been successfully applied to several practical problems such as diagnosis. In this paper we investigate whether the computational complexity of abduction can be reduced by an appropriate use of preprocessing or compilation. This is motivated by the fact that part of the data of the problem (namely, the set of all possible assumptions and the theory relating assumptions and manifestations) are often known before the rest of the problem. We present a detailed analysis of the computational complexity of abduction when compilation is allowed. Introduction Abduction is, along with deduction and induction, one of the main reasoning styles. The first researcher to study abduction in detail has been C. S. Peirce (1955). The simplest presentation of abduction is by comparing it with deduction and induction. Deduction is the process of obtaining conclusions from facts and rules, so, for instance, from a and a # b ...
