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

Resource-based Planning with Timelines

Real world planning applications typically involve making decisions that consumes limited resources, which requires both planning and scheduling. In this paper we propose a new approach that bridges the gap between planning and scheduling by explicitly modeling the problem in terms of resources, state variables and actions. We show that it is an intuitive way to formulate real world problems with complex constraints, and that solutions can be found by compiling the problem into a constraint satisfaction problem

Evaluating Cases in Legal Disputes as Rival Theories

In this paper we propose to draw a link from the quantitative notion of coherence, previously used to evaluate rival scientific theories, to legal reasoning. We evaluate the stories of the plaintiff and the defendant in a legal case as rival theories by measuring how well they cohere when accounting for the evidence. We show that this gives rise to a formalized comparison between rival cases that account for the same set of evidence, and provide a possible explanation as to why judgements may favour one side over the other. We illustrate our approach by applying it to a known legal dispute from the literature

Eliciting Truthful Measurements from a Community of Sensors

As the Internet of Things grows to large scale, its components will increasingly be controlled by selfinterested agents. For example, sensor networks will evolve to community sensing where a community of agents combine their data into a single coherent structure. As there is no central quality control, agents need to be incentivized to provide accurate measurements. We propose game-theoretic mechanisms that provide such incentives and show their application on the example of community sensing for monitoring air pollution. These mechanisms can be applied to most sensing scenarios and allow the Internet of Things to grow to much larger scale than currently exists

Restarts and Nogood Recording in Qualitative Constraint-based Reasoning

This paper introduces restart and nogood recording techniques in the domain of qualitative spatial and temporal reasoning. Nogoods and restarts can be applied orthogonally to usual methods for solving qualitative constraint satisfaction problems. In particular, we propose a more general definition of nogoods that allows for exploiting information about nogoods and tractable subclasses during backtracking search. First evaluations of the proposed techniques show promising results

A Divide-and-Conquer Approach for Solving Interval Algebra Networks

Deciding consistency of constraint networks is a fundamental problem in qualitative spatial and temporal reasoning. In this paper we introduce a divide-and-conquer method that recursively partitions a given problem into smaller sub-problems in deciding consistency. We identify a key theoretical property of a qualitative calculus that ensures the soundness and completeness of this method, and show that it is satisfied by the Interval Algebra (IA) and the Point Algebra (PA). We develop a new encoding scheme for IA networks based on a combination of our divide-and-conquer method with an existing encoding of IA networks into SAT. We empirically show that our new encoding scheme scales to much larger problems and exhibits a consistent and significant improvement in efficiency over state-of-the-art solvers on the most difficult instances

The Coherence of Theories-Dependencies and Weights

One way to evaluate and compare rival but potentially incompatible theories that account for the same set of observations is coherence. In this paper we take the quantitative notion of theory coherence as proposed by [Kwok, et.al. 98] and broaden its foundations. The generalisation will give a measure of the efficacy of a sub–theory as against single theory components. This also gives rise to notions of dependencies and couplings to account for how theory components interact with each other. Secondly we wish to capture the fact that not all components within a theory are of equal importance. To do this we assign weights to theory components. This framework is applied to game theory and the performance of a coherentist player is investigated within the iterated Prisoner’s Dilemma

Efficient methods for qualitative spatial and temporal reasoning

Qualitative aspects of spatial or temporal information such as the distance between points, duration between events, and topology between regions can be modelled by a qualitative calculus. It represent the relations between various entities in space or time by a set of base relations, and ambiguity or incomplete knowledge can be expressed as a disjunction of different possible base relations. This thesis investigates the reasoning problem of such qualitative spatial or temporal calculi, where the task is to determine whether a given set of spatial or temporal information is consistent. The main challenge is to deal with the large number of possible relations between the spatial or temporal entities, and to find the solution in an efficient manner. This thesis approaches this challenge from several directions. We first investigate if there are some relations in a qualitative calculus which could form constraint networks that make the reasoning problem difficult. This would help us to determine whether tractable reasoning is actually possible. Secondly, we investigate algebraic properties of a qualitative calculus. We present a condition of the qualitative calculus that ensures no inconsistencies can be introduced when combining two constraint networks that share information in common. Thirdly, we reverse this process to decompose a constraint network into many smaller components to decide consistency. We evaluate our results using a well known qualitative temporal calculus, Allen's Interval Algebra, and show that this leads to a significant improvement to current state of the art. Finally, we apply the network decomposition approach to large qualitative calculi such as Rectangle Algebra and Block Algebra. The latter was previously considered too large for any efficient reasoning. We show that our approach works well for most instances of these calculi, and that efficient reasoning with these highly expressive spatial calculi is indeed possible