Interval-based Synthesis

We introduce the synthesis problem for Halpern and Shoham's modal logic of intervals extended with an equivalence relation over time points, abbreviated HSeq. In analogy to the case of monadic second-order logic of one successor, the considered synthesis problem receives as input an HSeq formula phi and a finite set Sigma of propositional variables and temporal requests, and it establishes whether or not, for all possible evaluations of elements in Sigma in every interval structure, there exists an evaluation of the remaining propositional variables and temporal requests such that the resulting structure is a model for phi. We focus our attention on decidability of the synthesis problem for some meaningful fragments of HSeq, whose modalities are drawn from the set A (meets), Abar (met by), B (begins), Bbar (begun by), interpreted over finite linear orders and natural numbers. We prove that the fragment ABBbareq is decidable (non-primitive recursive hard), while the fragment AAbarBBbar turns out to be undecidable. In addition, we show that even the synthesis problem for ABBbar becomes undecidable if we replace finite linear orders by natural numbers.Comment: In Proceedings GandALF 2014, arXiv:1408.556

Temporalized logics and automata for time granularity

Suitable extensions of the monadic second-order theory of k successors have been proposed in the literature to capture the notion of time granularity. In this paper, we provide the monadic second-order theories of downward unbounded layered structures, which are infinitely refinable structures consisting of a coarsest domain and an infinite number of finer and finer domains, and of upward unbounded layered structures, which consist of a finest domain and an infinite number of coarser and coarser domains, with expressively complete and elementarily decidable temporal logic counterparts. We obtain such a result in two steps. First, we define a new class of combined automata, called temporalized automata, which can be proved to be the automata-theoretic counterpart of temporalized logics, and show that relevant properties, such as closure under Boolean operations, decidability, and expressive equivalence with respect to temporal logics, transfer from component automata to temporalized ones. Then, we exploit the correspondence between temporalized logics and automata to reduce the task of finding the temporal logic counterparts of the given theories of time granularity to the easier one of finding temporalized automata counterparts of them.Comment: Journal: Theory and Practice of Logic Programming Journal Acronym: TPLP Category: Paper for Special Issue (Verification and Computational Logic) Submitted: 18 March 2002, revised: 14 Januari 2003, accepted: 5 September 200

Case Adaptation with Qualitative Algebras

This paper proposes an approach for the adaptation of spatial or temporal cases in a case-based reasoning system. Qualitative algebras are used as spatial and temporal knowledge representation languages. The intuition behind this adaptation approach is to apply a substitution and then repair potential inconsistencies, thanks to belief revision on qualitative algebras. A temporal example from the cooking domain is given. (The paper on which this extended abstract is based was the recipient of the best paper award of the 2012 International Conference on Case-Based Reasoning.

On (Some) Explanations in Physics

I offer one possible explanation of why inertial and gravitational mass are equal in Newtonian gravitation. I then argue that this is an example of a kind of explanation that is not captured by standard philosophical accounts of scientific explanation. Moreover, this form of explanation is particularly important, at least in physics, because demands for this kind of explanation are used to motivate and shape research into the next generation of physical theories. I suggest that explanations of the sort I describe reveal something important about one way in which physical theories can be related diachronically.Comment: 32 pages. Forthcoming in Philosophy of Scienc

A General Framework for Representing, Reasoning and Querying with Annotated Semantic Web Data

We describe a generic framework for representing and reasoning with annotated Semantic Web data, a task becoming more important with the recent increased amount of inconsistent and non-reliable meta-data on the web. We formalise the annotated language, the corresponding deductive system and address the query answering problem. Previous contributions on specific RDF annotation domains are encompassed by our unified reasoning formalism as we show by instantiating it on (i) temporal, (ii) fuzzy, and (iii) provenance annotations. Moreover, we provide a generic method for combining multiple annotation domains allowing to represent, e.g. temporally-annotated fuzzy RDF. Furthermore, we address the development of a query language -- AnQL -- that is inspired by SPARQL, including several features of SPARQL 1.1 (subqueries, aggregates, assignment, solution modifiers) along with the formal definitions of their semantics

A decidable weakening of Compass Logic based on cone-shaped cardinal directions

We introduce a modal logic, called Cone Logic, whose formulas describe properties of points in the plane and spatial relationships between them. Points are labelled by proposition letters and spatial relations are induced by the four cone-shaped cardinal directions. Cone Logic can be seen as a weakening of Venema's Compass Logic. We prove that, unlike Compass Logic and other projection-based spatial logics, its satisfiability problem is decidable (precisely, PSPACE-complete). We also show that it is expressive enough to capture meaningful interval temporal logics - in particular, the interval temporal logic of Allen's relations "Begins", "During", and "Later", and their transposes

Interval vs. Point Temporal Logic Model Checking: an Expressiveness Comparison

Model checking is a powerful method widely explored in formal verification to check the (state-transition) model of a system against desired properties of its behaviour. Classically, properties are expressed by formulas of a temporal logic, such as LTL, CTL, and CTL*. These logics are "point-wise" interpreted, as they describe how the system evolves state-by-state. On the contrary, Halpern and Shoham\u27s interval temporal logic (HS) is "interval-wise" interpreted, thus allowing one to naturally express properties of computation stretches, spanning a sequence of states, or properties involving temporal aggregations, which are inherently "interval-based". In this paper, we study the expressiveness of HS in model checking, in comparison with that of the standard logics LTL, CTL, and CTL*. To this end, we consider HS endowed with three semantic variants: the state-based semantics, introduced by Montanari et al., which allows branching in the past and in the future, the linear-past semantics, allowing branching only in the future, and the linear semantics, disallowing branching. These variants are compared, as for their expressiveness, among themselves and to standard temporal logics, getting a complete picture. In particular, HS with linear (resp., linear-past) semantics is proved to be equivalent to LTL (resp., finitary CTL*)