The ability to "define" propositions using default assumptions about the same propositions is ide... more The ability to "define" propositions using default assumptions about the same propositions is identified as a significant source of computational complexity in nonmonotonic reasoning. If such constructs are not allowed, i.e. the knowledge base is stratified, a notable computational advantage is obtained. This is demonstrated by developing an iterative algorithm for propositional stratified autoepistemic theories the complexity of which is dominated by required classical reasoning. Thus efficient subclasses of stratified nonmonotonic reasoning can be obtained by further restricting the form of sentences in the knowledge base. As an example quadratic and linear time algorithms are derived for specific subclasses of stratified autoepistemic theories. The results are shown to imply efficient reasoning methods for stratified cases of default logic, logic programs, truth maintenance systems, and nonmonotonic modal logics. * This paper was first published as (Niemel~ and Rintanen, 1992). ** Ilkka Niemel~ gratefully acknowledges the support from the following foundations: Foundation of Technology, Jenny and Antti Wihuri Foundation, Emil Aaltonen Foundation, Alfred Kordelin Foundation, Heikki and Hilma Honkanen Foundation.
This paper investigates the problem of nding subclasses of nonmonotonic reasoning which can be im... more This paper investigates the problem of nding subclasses of nonmonotonic reasoning which can be implemented eOEciently. The ability to idenej propositions using default assumptions about the same propositions is identied as a major source of computational complexity in nonmonotonic reasoning. If such constructs are not allowed, i.e. stratied knowledge bases are considered, a signicant computational advantage is obtained. This is demonstrated by developing an iterative algorithm for propositional stratied autoepistemic theories the complexity of which is dominated by required classical reasoning. Thus eOEcient subclasses of stratied nonmonotonic reasoning can be obtained by further restricting the form of sentences in a knowledge base. As an example quadratic and linear time algorithms for specic subclasses of stratied autoepistemic theories are derived. The results are shown to imply eOEcient reasoning methods for stratied cases of default logic, logic programs, truth maintenance sys...
Many knowledge representation tasks involve trees or similar structures as abstract datatypes. Ho... more Many knowledge representation tasks involve trees or similar structures as abstract datatypes. However, devising compact and efficient declarative representations of such structural properties is non-obvious and can be challenging indeed. In this paper, we take a number of acyclicity properties into consideration and investigate various logic-based approaches to encode them. We use answer set programming as the primary representation language but also consider mappings to related formalisms, such as propositional logic, difference logic, and linear programming. We study the compactness of encodings and the resulting computational performance on benchmarks involving acyclic or tree structures.
Many knowledge representation tasks involve trees or similar structures as abstract datatypes. Ho... more Many knowledge representation tasks involve trees or similar structures as abstract datatypes. However, devising compact and efficient declarative representations of such properties is non-obvious and can be challenging indeed. In this paper, we take acyclicity properties into consideration and investigate logic-based approaches to encode them. We use answer set programming as the primary representation language but also consider mappings to related formalisms, such as propositional logic, difference logic, and linear programming.
Answer set programming (ASP) is a declarative programming paradigm for solving search problems ar... more Answer set programming (ASP) is a declarative programming paradigm for solving search problems arising in knowledge-intensive domains. One viable way to implement the computation of answer sets corresponding to problem solutions is to recast a logic program as a Boolean satisfiability (SAT) problem and to use existing SAT solver technology for the actual search. Such mappings can be obtained by augmenting Clark's completion with constraints guaranteeing the strong justifiability of answer sets. To this end, we consider an extension of SAT by graphs subject to an acyclicity constraint, called SAT modulo acyclicity. We devise a linear embedding of logic programs and study the performance of answer set computation with SAT modulo acyclicity solvers. 1 The support from the Finnish Centre of Excellence in Computational Inference Research (COIN) funded by the Academy of Finland (under grant #251170) is gratefully acknowledged.
During the past several years, AI planning has made major steps forward in terms of the size and ... more During the past several years, AI planning has made major steps forward in terms of the size and difficulty of problems that can be solved. In this article we give an overview of the techniques that have been part of the recent developments. Instead of concentrating on individual planning systems, we review the underlying principles behind many of the successful planners. Most of the overview is devoted to classical planning, that is fully deterministic planning with one initial state, and we discuss more general forms of planning only briefly in the end of the article.
We investigate the problem of learning the structure of a Markov network from data. It is shown t... more We investigate the problem of learning the structure of a Markov network from data. It is shown that the structure of such networks can be described in terms of constraints which enables the use of existing solver technology with optimization capabilities to compute optimal networks starting from initial scores computed from the data. To achieve efficient encodings, we develop a novel characterization of Markov network structure using a balancing condition on the separators between cliques forming the network. The resulting translations into propositional satisfiability and its extensions such as maximum satisfiability, satisfiability modulo theories, and answer set programming, enable us to prove optimal certain network structures which have been previously found by stochastic search. 1
Proceedings of the 5th European Conference on Planning Recent Advances in Ai Planning, Sep 8, 1999
We extend a planning algorithm to cover simple forms of arithmetics. The operator preconditions c... more We extend a planning algorithm to cover simple forms of arithmetics. The operator preconditions can refer to the values of numeric variables and the operator postconditions can modify the values of numeric variables. The basis planning algorithm is based on techniques from propositional satisfiability testing and does not restrict to forward or backward chaining. When several operations affect a numeric variable by increasing and decreasing its value in parallel, the effects have to be combined in a meaningful way. This problem is especially acute in planning algorithms that maintain an incomplete state description of every time point of a plan execution. The approach we take requires that for operators that are executed in parallel, all linearizations of the operations to total orders behave equivalently. We provide an efficient and general solution to the problem.
Statistical model learning problems are traditionally solved using either heuristic greedy optimi... more Statistical model learning problems are traditionally solved using either heuristic greedy optimization or stochastic simulation, such as Markov chain Monte Carlo or simulated annealing. Recently, there has been an increasing interest in the use of combinatorial search methods, including those based on computational logic. Some of these methods are particularly attractive since they can also be successful in proving the global optimality of solutions, in contrast to stochastic algorithms that only guarantee optimality at the limit. Here we improve and generalize a recently introduced constraint-based method for learning undirected graphical models. The new method combines perfect elimi
We extend a planning algorithm to cover simple forms of arithmetics. The operator preconditions c... more We extend a planning algorithm to cover simple forms of arithmetics. The operator preconditions can refer to the values of numeric variables and the operator postconditions can modify the values of numeric variables. The basis planning algorithm is based on techniques from propositional satisfiability testing and does not restrict to forward or backward chaining. When several operations affect a numeric variable by increasing and decreasing its value in parallel, the effects have to be combined in a meaningful way. This problem is especially acute in planning algorithms that maintain an incomplete state description of every time point of a plan execution. The approach we take requires that for operators that are executed in parallel, all linearizations of the operations to total orders behave equivalently. We provide an efficient and general solution to the problem.
We investigate the problem of learning the structure of a Markov network from data. It is shown t... more We investigate the problem of learning the structure of a Markov network from data. It is shown that the structure of such networks can be described in terms of constraints which enables the use of existing solver technology with optimization capabilities to compute optimal networks starting from initial scores computed from the data. To achieve efficient encodings, we develop a novel characterization of Markov network structure using a balancing condition on the separators between cliques forming the network. The resulting translations into propositional satisfiability and its extensions such as maximum satisfiability, satisfiability modulo theories, and answer set programming, enable us to prove optimal certain network structures which have been previously found by stochastic search. 1
The ability to "define" propositions using default assumptions about the same propositions is ide... more The ability to "define" propositions using default assumptions about the same propositions is identified as a significant source of computational complexity in nonmonotonic reasoning. If such constructs are not allowed, i.e. the knowledge base is stratified, a notable computational advantage is obtained. This is demonstrated by developing an iterative algorithm for propositional stratified autoepistemic theories the complexity of which is dominated by required classical reasoning. Thus efficient subclasses of stratified nonmonotonic reasoning can be obtained by further restricting the form of sentences in the knowledge base. As an example quadratic and linear time algorithms are derived for specific subclasses of stratified autoepistemic theories. The results are shown to imply efficient reasoning methods for stratified cases of default logic, logic programs, truth maintenance systems, and nonmonotonic modal logics. * This paper was first published as (Niemel~ and Rintanen, 1992). ** Ilkka Niemel~ gratefully acknowledges the support from the following foundations: Foundation of Technology, Jenny and Antti Wihuri Foundation, Emil Aaltonen Foundation, Alfred Kordelin Foundation, Heikki and Hilma Honkanen Foundation.
This paper investigates the problem of nding subclasses of nonmonotonic reasoning which can be im... more This paper investigates the problem of nding subclasses of nonmonotonic reasoning which can be implemented eOEciently. The ability to idenej propositions using default assumptions about the same propositions is identied as a major source of computational complexity in nonmonotonic reasoning. If such constructs are not allowed, i.e. stratied knowledge bases are considered, a signicant computational advantage is obtained. This is demonstrated by developing an iterative algorithm for propositional stratied autoepistemic theories the complexity of which is dominated by required classical reasoning. Thus eOEcient subclasses of stratied nonmonotonic reasoning can be obtained by further restricting the form of sentences in a knowledge base. As an example quadratic and linear time algorithms for specic subclasses of stratied autoepistemic theories are derived. The results are shown to imply eOEcient reasoning methods for stratied cases of default logic, logic programs, truth maintenance sys...
Many knowledge representation tasks involve trees or similar structures as abstract datatypes. Ho... more Many knowledge representation tasks involve trees or similar structures as abstract datatypes. However, devising compact and efficient declarative representations of such structural properties is non-obvious and can be challenging indeed. In this paper, we take a number of acyclicity properties into consideration and investigate various logic-based approaches to encode them. We use answer set programming as the primary representation language but also consider mappings to related formalisms, such as propositional logic, difference logic, and linear programming. We study the compactness of encodings and the resulting computational performance on benchmarks involving acyclic or tree structures.
Many knowledge representation tasks involve trees or similar structures as abstract datatypes. Ho... more Many knowledge representation tasks involve trees or similar structures as abstract datatypes. However, devising compact and efficient declarative representations of such properties is non-obvious and can be challenging indeed. In this paper, we take acyclicity properties into consideration and investigate logic-based approaches to encode them. We use answer set programming as the primary representation language but also consider mappings to related formalisms, such as propositional logic, difference logic, and linear programming.
Answer set programming (ASP) is a declarative programming paradigm for solving search problems ar... more Answer set programming (ASP) is a declarative programming paradigm for solving search problems arising in knowledge-intensive domains. One viable way to implement the computation of answer sets corresponding to problem solutions is to recast a logic program as a Boolean satisfiability (SAT) problem and to use existing SAT solver technology for the actual search. Such mappings can be obtained by augmenting Clark's completion with constraints guaranteeing the strong justifiability of answer sets. To this end, we consider an extension of SAT by graphs subject to an acyclicity constraint, called SAT modulo acyclicity. We devise a linear embedding of logic programs and study the performance of answer set computation with SAT modulo acyclicity solvers. 1 The support from the Finnish Centre of Excellence in Computational Inference Research (COIN) funded by the Academy of Finland (under grant #251170) is gratefully acknowledged.
During the past several years, AI planning has made major steps forward in terms of the size and ... more During the past several years, AI planning has made major steps forward in terms of the size and difficulty of problems that can be solved. In this article we give an overview of the techniques that have been part of the recent developments. Instead of concentrating on individual planning systems, we review the underlying principles behind many of the successful planners. Most of the overview is devoted to classical planning, that is fully deterministic planning with one initial state, and we discuss more general forms of planning only briefly in the end of the article.
We investigate the problem of learning the structure of a Markov network from data. It is shown t... more We investigate the problem of learning the structure of a Markov network from data. It is shown that the structure of such networks can be described in terms of constraints which enables the use of existing solver technology with optimization capabilities to compute optimal networks starting from initial scores computed from the data. To achieve efficient encodings, we develop a novel characterization of Markov network structure using a balancing condition on the separators between cliques forming the network. The resulting translations into propositional satisfiability and its extensions such as maximum satisfiability, satisfiability modulo theories, and answer set programming, enable us to prove optimal certain network structures which have been previously found by stochastic search. 1
Proceedings of the 5th European Conference on Planning Recent Advances in Ai Planning, Sep 8, 1999
We extend a planning algorithm to cover simple forms of arithmetics. The operator preconditions c... more We extend a planning algorithm to cover simple forms of arithmetics. The operator preconditions can refer to the values of numeric variables and the operator postconditions can modify the values of numeric variables. The basis planning algorithm is based on techniques from propositional satisfiability testing and does not restrict to forward or backward chaining. When several operations affect a numeric variable by increasing and decreasing its value in parallel, the effects have to be combined in a meaningful way. This problem is especially acute in planning algorithms that maintain an incomplete state description of every time point of a plan execution. The approach we take requires that for operators that are executed in parallel, all linearizations of the operations to total orders behave equivalently. We provide an efficient and general solution to the problem.
Statistical model learning problems are traditionally solved using either heuristic greedy optimi... more Statistical model learning problems are traditionally solved using either heuristic greedy optimization or stochastic simulation, such as Markov chain Monte Carlo or simulated annealing. Recently, there has been an increasing interest in the use of combinatorial search methods, including those based on computational logic. Some of these methods are particularly attractive since they can also be successful in proving the global optimality of solutions, in contrast to stochastic algorithms that only guarantee optimality at the limit. Here we improve and generalize a recently introduced constraint-based method for learning undirected graphical models. The new method combines perfect elimi
We extend a planning algorithm to cover simple forms of arithmetics. The operator preconditions c... more We extend a planning algorithm to cover simple forms of arithmetics. The operator preconditions can refer to the values of numeric variables and the operator postconditions can modify the values of numeric variables. The basis planning algorithm is based on techniques from propositional satisfiability testing and does not restrict to forward or backward chaining. When several operations affect a numeric variable by increasing and decreasing its value in parallel, the effects have to be combined in a meaningful way. This problem is especially acute in planning algorithms that maintain an incomplete state description of every time point of a plan execution. The approach we take requires that for operators that are executed in parallel, all linearizations of the operations to total orders behave equivalently. We provide an efficient and general solution to the problem.
We investigate the problem of learning the structure of a Markov network from data. It is shown t... more We investigate the problem of learning the structure of a Markov network from data. It is shown that the structure of such networks can be described in terms of constraints which enables the use of existing solver technology with optimization capabilities to compute optimal networks starting from initial scores computed from the data. To achieve efficient encodings, we develop a novel characterization of Markov network structure using a balancing condition on the separators between cliques forming the network. The resulting translations into propositional satisfiability and its extensions such as maximum satisfiability, satisfiability modulo theories, and answer set programming, enable us to prove optimal certain network structures which have been previously found by stochastic search. 1
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