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A case study of expressively constrainable level design automation tools for a puzzle game
 In Proceedings of the Conference on Foundations of Digital Games
, 2012
"... Some problems in procedural content generation for games involve hard constraints (e.g. that a generated puzzle is necessarily solvable). Common techniques for generator design lack a way to specify crisp (yes/no) constraints on what counts as a valid content artifact and guarantee these constraints ..."
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Some problems in procedural content generation for games involve hard constraints (e.g. that a generated puzzle is necessarily solvable). Common techniques for generator design lack a way to specify crisp (yes/no) constraints on what counts as a valid content artifact and guarantee these constraints are satisfied in the generator’s output. In this paper we present two independent implementations of three diverse level design automation tools for the popular online educational game Refraction. All of the systems guarantee key properties of their output. Applying a constraintfocused generator design perspective in depth, we found that even emergent aesthetic style properties were straightforward to directly control. Our results with Refraction provide further concrete evidence for the claim that the expressive power of constraints and the ease with which they can be incorporated into suitably designed generative processes makes them a powerful tool for producing reliablycontrollable generators for game content.
Conflictdriven answer set enumeration
, 2007
"... We elaborate upon a recently proposed approach to finding an answer set of a logic program based on concepts from constraint processing and satisfiability checking. We extend this approach and propose a new algorithm for enumerating answer sets. The algorithm, which to our knowledge is novel even in ..."
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Cited by 13 (9 self)
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We elaborate upon a recently proposed approach to finding an answer set of a logic program based on concepts from constraint processing and satisfiability checking. We extend this approach and propose a new algorithm for enumerating answer sets. The algorithm, which to our knowledge is novel even in the context of satisfiability checking, is implemented in the clasp answer set solver. We contrast our new approach to alternative systems and different options of clasp, and provide an empirical evaluation.
Advanced Preprocessing for Answer Set Solving
"... Abstract. We introduce the first substantial approach to preprocessing in the context of answer set solving. The idea is to simplify a logic program while identifying equivalences among its relevant constituents. These equivalences are then used for building a compact representation of the program ( ..."
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Cited by 12 (5 self)
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Abstract. We introduce the first substantial approach to preprocessing in the context of answer set solving. The idea is to simplify a logic program while identifying equivalences among its relevant constituents. These equivalences are then used for building a compact representation of the program (in terms of Boolean constraints). We implemented our approach as well as a SATbased technique to reduce Boolean constraints. This allows us to empirically analyze both preprocessing types and to demonstrate their computational impact. 1
On the relation of constraint answer set programming languages and algorithms
 in AAAI
, 2012
"... Recently a logic programming language AC was proposed by Mellarkod et al. (2008) to integrate answer set programming (ASP) and constraint logic programming. Similarly, Gebser et al. (2009) proposed a CLINGCON language integrating ASP and finite domain constraints. These languages allow new efficient ..."
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Recently a logic programming language AC was proposed by Mellarkod et al. (2008) to integrate answer set programming (ASP) and constraint logic programming. Similarly, Gebser et al. (2009) proposed a CLINGCON language integrating ASP and finite domain constraints. These languages allow new efficient inference algorithms that combine traditional ASP procedures and other methods in constraint programming. In this paper we show that a transition system introduced by Nieuwenhuis et al. (2006) to model SAT solvers can be extended to model the “hybrid ” ACSOLVER algorithm by Mellarkod et al. developed for simple AC programs and the CLINGCON algorithm by Gebser et al. for clingcon programs. We define weaklysimple programs and show how the introduced transition systems generalize the ACSOLVER and CLINGCON algorithms to such programs. Finally, we state the precise relation between AC and CLINGCON languages and the ACSOLVER and CLINGCON algorithms.
Quantifying over Play: Constraining Undesirable Solutions in Puzzle Design
"... Motivated by our ongoing efforts in the development of Refraction 2, a puzzle game targeting mathematics education, we realized that the quality of a puzzle is critically sensitive to the presence of alternative solutions with undesirable properties. Where, in our game, we seek a way to automaticall ..."
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Motivated by our ongoing efforts in the development of Refraction 2, a puzzle game targeting mathematics education, we realized that the quality of a puzzle is critically sensitive to the presence of alternative solutions with undesirable properties. Where, in our game, we seek a way to automatically synthesize puzzles that can only be solved if the player demonstrates specific concepts, concern for the possibility of undesirable play touches other interactive design domains. To frame this problem (and our solution to it) in a general context, we formalize the problem of generating solvable puzzles that admit no undesirable solutions as an NP NPcomplete search problem. By making two designoriented extensions to answer set programming (a technology that has been recently applied to constrained game content generation problems) we offer a general way to declaratively pose and automatically solve the highcomplexity problems coming from this formulation. Applying this technique to Refraction, we demonstrate a qualitative leap in the kind of puzzles we can reliably generate. This work opens up new possibilities for qualityfocused content generators that guarantee properties over their entire combinatorial space of play.
On the Implementation of Weight Constraint Rules in ConflictDriven ASP Solvers
"... Abstract. We present the first comprehensive approach to integrating cardinality and weight rules into conflictdriven ASP solving. We begin with a uniform, constraintbased characterization of answer sets in terms of nogoods. This provides the semantic underpinnings of our approach in fixing all ne ..."
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Abstract. We present the first comprehensive approach to integrating cardinality and weight rules into conflictdriven ASP solving. We begin with a uniform, constraintbased characterization of answer sets in terms of nogoods. This provides the semantic underpinnings of our approach in fixing all necessary inferences that must be supported by an appropriate implementation. We then provide key algorithms detailing the salient features needed for implementing weight constraint rules. This involves a sophisticated unfounded set checker as well as an extended propagation algorithm along with the underlying data structures. We implemented our techniques within the ASP solver clasp and demonstrate their effectiveness by an experimental evaluation. 1
Decomposition of Distributed Nonmonotonic MultiContext Systems
"... MultiContext Systems (MCS) are formalisms that enable the interlinkage of single knowledge bases, called contexts, via bridge rules. Recently, the evaluation of heterogeneous, nonmonotonic MCS was considered in DaoTran et al. (2010), where a fully distributed algorithm was described. In this paper ..."
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Cited by 11 (7 self)
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MultiContext Systems (MCS) are formalisms that enable the interlinkage of single knowledge bases, called contexts, via bridge rules. Recently, the evaluation of heterogeneous, nonmonotonic MCS was considered in DaoTran et al. (2010), where a fully distributed algorithm was described. In this paper, we continue this line of work and present a decomposition technique for MCS which analyzes the topology of an MCS. It applies pruning techniques to get economically small representations of context dependencies. Orthogonal to this, we characterize minimal interfaces for information exchange between contexts, such that data transmissions can be minimized. We then present a novel evaluation algorithm that operates on a query plan which is compiled with topology pruning and interface minimization. The effectiveness of the optimization techniques is demonstrated by a prototype implementation, which uses an offtheshelf SAT solver and shows encouraging experimental results.
IndustrialSize Scheduling with ASP+CP
"... Abstract Answer Set Programming (ASP) combines a powerful, theoretically principled knowledge representation formalism and powerful solvers. To improve efficiency of computation on certain classes of problems, researchers have recently developed hybrid languages and solvers, combining ASP with langu ..."
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Abstract Answer Set Programming (ASP) combines a powerful, theoretically principled knowledge representation formalism and powerful solvers. To improve efficiency of computation on certain classes of problems, researchers have recently developed hybrid languages and solvers, combining ASP with language constructs and solving techniques from Constraint Programming (CP). The resulting ASP+CP solvers exhibit remarkable performance on “toy ” problems. To the best of our knowledge, however, no hybrid ASP+CP language and solver have been used in practical, industrialsize applications. In this paper, we report on the first such successful application, consisting of the use of the hybrid ASP+CP system ezcsp to solve sophisticated industrialsize scheduling problems. 1
Computing Loops with at Most One External Support Rule for Disjunctive Logic Programs
"... Abstract. We extend to disjunctive logic programs our previous work on computing loop formulas of loops with at most one external support. We show that for these logic programs, loop formulas of loops with no external support can be computed in polynomial time, and if the given program has no constr ..."
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Abstract. We extend to disjunctive logic programs our previous work on computing loop formulas of loops with at most one external support. We show that for these logic programs, loop formulas of loops with no external support can be computed in polynomial time, and if the given program has no constraints, an iterative procedure based on these formulas, the program completion, and unit propagation computes the least fixed point of a simplification operator used by DLV. We also relate loops with no external supports to the unfounded sets and the wellfounded semantics of disjunctive logic programs by Wang and Zhou. However, the problem of computing loop formulas of loops with at most one external support rule is NPhard for disjunctive logic programs. We thus propose a polynomial algorithm for computing some of these loop formulas, and show experimentally that this polynomial approximation algorithm can be effective in practice. 1
Predicate logic as a modelling language: The IDP system
, 2014
"... per Predicate Logic as a Programming Language was a breakthrough for the use of logic in computer science. The more recent tremendous progress in automated reasoning technologies, particularly in SAT solving and Constraint Programming, has paved the way for the use of logic as a modelling language. ..."
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per Predicate Logic as a Programming Language was a breakthrough for the use of logic in computer science. The more recent tremendous progress in automated reasoning technologies, particularly in SAT solving and Constraint Programming, has paved the way for the use of logic as a modelling language. This paper describes the realisation of such a modelling language as the IDP knowledgebase system (KBS). In contrast to declarative programming, the user only specifies her knowledge about a problem and has not to pay attention to control issues. In the IDP system, declarative modelling is done in the language FO(·)IDP which combines inductive definitions (similar to sets of Prolog rules) with firstorder logic, types and aggregates, allowing for concise specifications. The paper presents the language, motivates the design choices and gives an overview of the system architecture and the implementation techniques. It also gives an overview of different inference tasks supported by the system such as query evaluation, model expansion and theorem proving, and explains in detail how combining various functionalities results in a stateoftheart model expansion engine. Finally, it explains how a tight integration with a procedural language (Lua) allows users to treat logical components as firstclass citizens and to solve complex problems in a workflow of (multiinference) interactions. 1