System aspmt2smt: Computing ASPMT Theories by SMT Solvers

Bartholomew, Michael; Lee, Joohyung

doi:10.1007/978-3-319-11558-0_37

Cited by 22 publications

(20 citation statements)

References 5 publications

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“…ASP Modulo extensions for handling specialised domains and abstraction mechanisms provides a powerful means for the utilising ASP as a foundational knowledge representation and reasoning (KR) method for a wide-range of application contexts. This approach is clearly demonstrated in work such as ASPMT [3,16,20], CLINGCON [14], ASPMT(QS) [34]. Most closely related to our research is the ASPMT founded non-monotonic spatial reasoning system ASPMT(QS) [34].…”

Section: Discussion and Related Worksupporting

confidence: 57%

“…Given a system of polynomial constraints over real variables X, the constraints are satisfiable if there exists some real value for each variable in X such that all the polynomial constraints are simultaneously satisfied. 3 For example, let point p be defined by real coordinates x p , y p , and let circle c be defined by the centre point x c , y c and real radius r c . A point p is incident to the interior of a circle c if the distance between p and the centre of c is less than the radius of c:…”

Section: Space-time Semantics As Polynomial Constraintsmentioning

confidence: 99%

“…Algebraic properties of ST relations are expressed as the following ASP rules and constraints. 4 (1) 3 The worst case complexity of solving a system of non-linear polynomial constraints over n real variables is O(2 2 n ) [2] owing to the Cylindrical Algebraic Decomposition algorithm [9], which is implemented in the solver z3 [10]. Although not relevant to this paper, it is worth pointing out that we use a (sound and complete) polynomial constraint solver that determines whether a system of non-linear polynomial constraints is satisfiable, based on an integration of Satisfiability Modulo Theories solver z3 [10] and numerical optimisation [30] with the library NLopt [19] using BOBYQA [25].…”

Section: Spatio-temporal Consistencymentioning

confidence: 99%

“…Most recently, there has been heightened interest to extend ASP in order to handle specialised domains and application-specific knowledge representation and reasoning (KR) capabilities. For instance, ASP Modulo Theories (ASPMT) go beyond the propositional setting of standard answer set programs by the integration of ASP with Satisfiability Modulo Theories (SMT) thereby facilitating reasoning about continuous domains [3,16,20]; using this approach, integrating knowledge sources of heterogeneous semantics (e.g., infinite domains) becomes possible. Similarly, CLINGCON [14] combines ASP with specialised constraint solvers supporting non-linear finite integers.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Answer Set Programming Modulo ‘Space-Time’

Schultz

Bhatt

Suchan

et al. 2018

Rules and Reasoning

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We present ASP Modulo 'Space-Time', a declarative representational and computational framework to perform commonsense reasoning about regions with both spatial and temporal components. Supported are capabilities for mixed qualitative-quantitative reasoning, consistency checking, and inferring compositions of space-time relations; these capabilities combine and synergise for applications in a range of AI application areas where the processing and interpretation of spatio-temporal data is crucial. The framework and resulting system is the only general KR-based method for declaratively reasoning about the dynamics of 'space-time' regions as first-class objects. We present an empirical evaluation (with scalability and robustness results), and include diverse application examples involving interpretation and control tasks.

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Section: Discussion and Related Worksupporting

confidence: 57%

Section: Space-time Semantics As Polynomial Constraintsmentioning

confidence: 99%

Section: Spatio-temporal Consistencymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Answer Set Programming Modulo ‘Space-Time’

Schultz

Bhatt

Suchan

et al. 2018

Rules and Reasoning

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“…no variable occurring in an argument of an uninterpreted function is related to the value variable of another uninterpreted function via equality [4]. The input program is divided into declarations of:…”

Section: Definition 11 (F-plain Formula) Let F Be a Function Constanmentioning

confidence: 99%

Logic Programming and Nonmonotonic Reasoning

Lang

2015

Lecture Notes in Computer Science

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Abstract. The systematic modelling of dynamic spatial systems [9] is a key requirement in a wide range of application areas such as comonsense cognitive robotics, computer-aided architecture design, dynamic geographic information systems. We present ASPMT(QS), a novel approach and fully-implemented prototype for non-monotonic spatial reasoning -a crucial requirement within dynamic spatial systems-based on Answer Set Programming Modulo Theories (ASPMT). ASPMT(QS) consists of a (qualitative) spatial representation module (QS) and a method for turning tight ASPMT instances into Sat Modulo Theories (SMT) instances in order to compute stable models by means of SMT solvers. We formalise and implement concepts of default spatial reasoning and spatial frame axioms using choice formulas. Spatial reasoning is performed by encoding spatial relations as systems of polynomial constraints, and solving via SMT with the theory of real nonlinear arithmetic. We empirically evaluate ASPMT(QS) in comparison with other prominent contemporary spatial reasoning systems. Our results show that ASPMT(QS) is the only existing system that is capable of reasoning about indirect spatial effects (i.e. addressing the ramification problem), and integrating geometric and qualitative spatial information within a non-monotonic spatial reasoning context.

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Lower Bound Founded Logic of Here-and-There

Calabar

Fandinno

Schaub

et al. 2019

Logics in Artificial Intelligence

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A distinguishing feature of Answer Set Programming is that all atoms belonging to a stable model must be founded. That is, an atom must not only be true but provably true. This can be made precise by means of the constructive logic of Here-and-There, whose equilibrium models correspond to stable models. One way of looking at foundedness is to regard Boolean truth values as ordered by letting true be greater than false. Then, each Boolean variable takes the smallest truth value that can be proven for it. This idea was generalized by Aziz to ordered domains and applied to constraint satisfaction problems. As before, the idea is that a, say integer, variable gets only assigned to the smallest integer that can be justified. In this paper, we present a logical reconstruction of Aziz' idea in the setting of the logic of Here-and-There. More precisely, we start by defining the logic of Here-and-There with lower bound founded variables along with its equilibrium models and elaborate upon its formal properties. Finally, we compare our approach with related ones and sketch future work.

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System aspmt2smt: Computing ASPMT Theories by SMT Solvers

Cited by 22 publications

References 5 publications

Answer Set Programming Modulo ‘Space-Time’

Answer Set Programming Modulo ‘Space-Time’

Logic Programming and Nonmonotonic Reasoning

Lower Bound Founded Logic of Here-and-There

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