Qualitative Spatial and Temporal Reasoning with Answer Set Programming

Representing and reasoning spatial and temporal information is a key research issue in Computer Science and Artificial Intelligence. In this paper, we introduce tools that produce three novel encodings which translate problems in qualitative spatial and temporal reasoning into logic programs for answer set programming solvers. Each encoding reflects a different type of modeling abstraction. We evaluate our approach with two of the most well known qualitative spatial and temporal reasoning formalisms, the Interval Algebra and Region Connection Calculus. Our results show some surprising findings, including the strong performance of the solver for disjunctive logic programs over the non-disjunctive ones on our benchmark problems

Answer Set Programming Modulo `Space-Time'

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

Reasoning about Qualitative Direction and Distance between Extended Objects using Answer Set Programming

In this thesis, we introduce a novel formal framework to represent and reason about qualitative direction and distance relations between extended objects using Answer Set Programming (ASP). We take Cardinal Directional Calculus (CDC) as a starting point and extend CDC with new sorts of constraints which involve defaults, preferences and negation. We call this extended version as nCDC. Then we further extend nCDC by augmenting qualitative distance relation and name this extension as nCDC+. For CDC, nCDC, nCDC+, we introduce an ASP-based general framework to solve consistency checking problems, address composition and inversion of qualitative spatial relations, infer unknown or missing relations between objects, and find a suitable configuration of objects which fulfills a given inquiry.Comment: In Proceedings ICLP 2019, arXiv:1909.0764

Answer Set Programming for Qualitative Spatio-temporal Reasoning: Methods and Experiments

We study the translation of reasoning problems involving qualitative spatio-temporal calculi into answer set programming (ASP). We present various alternative transformations and provide a qualitative comparison among them. An implementation of these transformations is provided by a tool that transforms problem instances specified in the language of the Generic Qualitative Reasoner (GQR) into ASP problems. Finally, we report on an experimental analysis of solving consistency problems for Allen’s Interval Algebra and the Region Connection Calculus with eight base relations (RCC-8)

A Generalised Approach for Encoding and Reasoning with Qualitative Theories in Answer Set Programming

Qualitative reasoning involves expressing and deriving knowledge based on qualitative terms such as natural language expressions, rather than strict mathematical quantities. Well over 40 qualitative calculi have been proposed so far, mostly in the spatial and temporal domains, with several practical applications such as naval traffic monitoring, warehouse process optimisation and robot manipulation. Even if a number of specialised qualitative reasoning tools have been developed so far, an important barrier to the wider adoption of these tools is that only qualitative reasoning is supported natively, when real-world problems most often require a combination of qualitative and other forms of reasoning. In this work, we propose to overcome this barrier by using ASP as a unifying formalism to tackle problems that require qualitative reasoning in addition to non-qualitative reasoning. A family of ASP encodings is proposed which can handle any qualitative calculus with binary relations. These encodings are experimentally evaluated using a real-world dataset based on a case study of determining optimal coverage of telecommunication antennas, and compared with the performance of two well-known dedicated reasoners. Experimental results show that the proposed encodings outperform one of the two reasoners, but fall behind the other, an acceptable trade-off given the added benefits of handling any type of reasoning as well as the interpretability of logic programs. This paper is under consideration for acceptance in TPLP.Comment: Paper presented at the 36th International Conference on Logic Programming (ICLP 2020), University Of Calabria, Rende (CS), Italy, September 2020, 18 pages, 3 figure

A Trajectory Calculus for Qualitative Spatial Reasoning Using Answer Set Programming

Spatial information is often expressed using qualitative terms such as natural language expressions instead of coordinates; reasoning over such terms has several practical applications, such as bus routes planning. Representing and reasoning on trajectories is a specific case of qualitative spatial reasoning that focuses on moving objects and their paths. In this work, we propose two versions of a trajectory calculus based on the allowed properties over trajectories, where trajectories are defined as a sequence of non-overlapping regions of a partitioned map. More specifically, if a given trajectory is allowed to start and finish at the same region, 6 base relations are defined (TC-6). If a given trajectory should have different start and finish regions but cycles are allowed within, 10 base relations are defined (TC-10). Both versions of the calculus are implemented as ASP programs; we propose several different encodings, including a generalised program capable of encoding any qualitative calculus in ASP. All proposed encodings are experimentally evaluated using a real-world dataset. Experiment results show that the best performing implementation can scale up to an input of 250 trajectories for TC-6 and 150 trajectories for TC-10 for the problem of discovering a consistent configuration, a significant improvement compared to previous ASP implementations for similar qualitative spatial and temporal calculi. This manuscript is under consideration for acceptance in TPLP.Comment: Paper presented at the 34th International Conference on Logic Programming (ICLP 2018), Oxford, UK, July 14 to July 17, 2018, 20 pages, LaTeX, 16 figure

Linear-Time Temporal Answer Set Programming

[Abstract]: In this survey, we present an overview on (Modal) Temporal Logic Programming in view of its application to Knowledge Representation and Declarative Problem Solving. The syntax of this extension of logic programs is the result of combining usual rules with temporal modal operators, as in Linear-time Temporal Logic (LTL). In the paper, we focus on the main recent results of the non-monotonic formalism called Temporal Equilibrium Logic (TEL) that is defined for the full syntax of LTL but involves a model selection criterion based on Equilibrium Logic, a well known logical characterization of Answer Set Programming (ASP). As a result, we obtain a proper extension of the stable models semantics for the general case of temporal formulas in the syntax of LTL. We recall the basic definitions for TEL and its monotonic basis, the temporal logic of Here-and-There (THT), and study the differences between finite and infinite trace length. We also provide further useful results, such as the translation into other formalisms like Quantified Equilibrium Logic and Second-order LTL, and some techniques for computing temporal stable models based on automata constructions. In the remainder of the paper, we focus on practical aspects, defining a syntactic fragment called (modal) temporal logic programs closer to ASP, and explaining how this has been exploited in the construction of the solver telingo, a temporal extension of the well-known ASP solver clingo that uses its incremental solving capabilities.Xunta de Galicia; ED431B 2019/03We are thankful to the anonymous reviewers for their thorough work and their useful suggestions that have helped to improve the paper. A special thanks goes to Mirosaw Truszczy´nski for his support in improving the quality of our paper. We are especially grateful to David Pearce, whose help and collaboration on Equilibrium Logic was the seed for a great part of the current paper. This work was partially supported by MICINN, Spain, grant PID2020-116201GB-I00, Xunta de Galicia, Spain (GPC ED431B 2019/03), R´egion Pays de la Loire, France, (projects EL4HC and etoiles montantes CTASP), European Union COST action CA-17124, and DFG grants SCHA 550/11 and 15, Germany

Qualitative Spatial and Temporal Reasoning with Answer Set Programming

Representing and reasoning spatial and temporal information is a key research issue in Computer Science and Artificial Intelligence. In this paper, we introduce tools that produce three novel encodings which translate problems in qualitative spatial and