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

Hybrid fragments of Halpern–Shoham logic and their expressive power

Halpern and Shoham modal logic of time intervals ( in short) is an elegant and highly influential propositional interval-based modal logic. Its sub-propositional fragments, that is fragments obtained by restricting use of propositional connectives, and their hybrid extensions with nominals and satisfaction operators have been recently studied and successfully applied in real-world use cases. Detailed investigation of their decidability and computational complexity has been conducted, however, there has been significantly less research on their expressive power. In this paper we make a step towards filling this gap. In particular, we (1) compare classes of frames definable in full and in its hybrid extension, and (2) determine in which sub-propositional -fragments we can express the difference operator, nominals, and satisfaction operators. The obtained results enable us to classify , its sub-propositional fragments, and their hybrid extensions according to their expressive power

Hybrid fragments of Halpern–Shoham logic and their expressive power

Halpern and Shoham modal logic of time intervals ( in short) is an elegant and highly influential propositional interval-based modal logic. Its sub-propositional fragments, that is fragments obtained by restricting use of propositional connectives, and their hybrid extensions with nominals and satisfaction operators have been recently studied and successfully applied in real-world use cases. Detailed investigation of their decidability and computational complexity has been conducted, however, there has been significantly less research on their expressive power. In this paper we make a step towards filling this gap. In particular, we (1) compare classes of frames definable in full and in its hybrid extension, and (2) determine in which sub-propositional -fragments we can express the difference operator, nominals, and satisfaction operators. The obtained results enable us to classify , its sub-propositional fragments, and their hybrid extensions according to their expressive power

Subject-oriented spatial logic

We present a modal logic for subject-oriented representation and reasoning about a two-dimensional space, which we call SOSL. The space is represented with the polar coordinate system where the subject occupies the central point and modal operators are interpreted by relations defined relatively to the position and orientation of the subject, namely ‘outwards’, ‘inwards’, ‘clockwise’, ‘counter-clockwise’, and the transitive closures of the first two. Such logic enables to express operators for the intrinsic relations: ‘in front’, ‘behind’, ‘to the left’, and ‘to the right’ of the subject, for the relative relations: ‘behind an object’, ‘between the subject and an object’, ‘to the left of an object’, and ‘to the right of an object’, and hybrid or distance operators. We prove that the satisfiability problem in SOSL is PSpace-complete, the same complexity holds over the classes of finite or infinite models, however, for models of fixed size the problem becomes NP-complete

Finitely materialisable Datalog programs with metric temporal operators

DatalogMTL is an extension of Datalog with metric temporal operators that has recently received significant attention. In contrast to plain Datalog, where scalable implementations are often based on materialisation (a.k.a. forward chaining), reasoning algorithms for recursive fragments of DatalogMTL are automata-based and not well suited for practice. In this paper we propose the class of finitely materialisable DatalogMTL programs, for which forward chaining reasoning terminates after finitely many rounds of rule application. We show that, for bounded programs (a large fragment of DatalogMTL where temporal intervals are restricted to not mention infinity), checking whether a program is finitely materialisable is feasible in exponential time, and propose sufficient conditions for finite materialisability that can be checked more efficiently. We finally show that fact entailment over finitely materialisable bounded programs is ExpTime-complete, and hence no harder than Datalog reasoning

DatalogMTL with negation under stable models semantics

We introduce negation under stable models semantics in DatalogMTL—a temporal extension of Datalog with metric operators. As a result, we obtain a rule language which combines the power of answer set programming with the temporal dimension provided by metric operators. We show that, in this setting, reasoning becomes undecidable over the rationals and decidable in EXPSPACE in data complexity over the integers. We also show that, if we restrict our attention to forward-propagating programs (where rules propagate information in a single temporal direction), reasoning over integers becomes PSPACE-complete in data complexity and hence no harder than over positive programs; however, reasoning over the rationals in this fragment remains undecidable

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