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

A General Framework for Automatic Termination Analysis of Logic Programs

This paper describes a general framework for automatic termination analysis of logic programs, where we understand by ``termination'' the finitenes s of the LD-tree constructed for the program and a given query. A general property of mappings from a certain subset of the branches of an infinite LD-tree into a finite set is proved. From this result several termination theorems are derived, by using different finite sets. The first two are formulated for the predicate dependency and atom dependency graphs. Then a general result for the case of the query-mapping pairs relevant to a program is proved (cf. \cite{Sagiv,Lindenstrauss:Sagiv}). The correctness of the {\em TermiLog} system described in \cite{Lindenstrauss:Sagiv:Serebrenik} follows from it. In this system it is not possible to prove termination for programs involving arithmetic predicates, since the usual order for the integers is not well-founded. A new method, which can be easily incorporated in {\em TermiLog} or similar systems, is presented, which makes it possible to prove termination for programs involving arithmetic predicates. It is based on combining a finite abstraction of the integers with the technique of the query-mapping pairs, and is essentially capable of dividing a termination proof into several cases, such that a simple termination function suffices for each case. Finally several possible extensions are outlined

UNDERSTANDING PREPOSITIONS THROUGH COGNITIVE GRAMMAR. A CASE OF IN

Poly - semantic nature of prepositions has been discussed in linguistic literature and confirmed by language data. In the majority of research within cognitive linguistics prepositions have been approached as predicates organising entities in space, with less attention paid to the search for a meaning schema sanctioning the numerous uses. Cognitive Grammar analytic tools allow for the analysis which results in discovering one meaning schema sanctioning the uses of the English preposition in. The present analysis is based on the assumption that the meaning schema of in profiles a relation of conceptual enclosure between two symbolic structures, one of which conceptually fits in the other. Accordingly, I argue that the speaker employs in to structure a real scene not because one element of the scene can physically enclose the other one, but due to conceptual ‘fitting in’ holding between the predication ‘preceding’ the preposition and the one that ‘follows’. In formal terms, the usage of in is conditioned and sanctioned by compatibility of active zones in the predications used to form the complex language expression involved. Peculiarities of physical organization may be ignored in such conceptualisation, though the speaker can choose to encode all peculiarities of physical organisation of real world objects employing different linguistic devices

Correlation of eigenstates in the critical regime of quantum Hall systems

We extend the multifractal analysis of the statistics of critical wave functions in quantum Hall systems by calculating numerically the correlations of local amplitudes corresponding to eigenstates at two different energies. Our results confirm multifractal scaling relations which are different from those occurring in conventional critical phenomena. The critical exponent corresponding to the typical amplitude, $\alpha_0\approx 2.28$, gives an almost complete characterization of the critical behavior of eigenstates, including correlations. Our results support the interpretation of the local density of states being an order parameter of the Anderson transition.Comment: 17 pages, 9 Postscript figure

Complexity Bounds for Ordinal-Based Termination

`What more than its truth do we know if we have a proof of a theorem in a given formal system?' We examine Kreisel's question in the particular context of program termination proofs, with an eye to deriving complexity bounds on program running times. Our main tool for this are length function theorems, which provide complexity bounds on the use of well quasi orders. We illustrate how to prove such theorems in the simple yet until now untreated case of ordinals. We show how to apply this new theorem to derive complexity bounds on programs when they are proven to terminate thanks to a ranking function into some ordinal.Comment: Invited talk at the 8th International Workshop on Reachability Problems (RP 2014, 22-24 September 2014, Oxford