On Relaxing Metric Information in Linear Temporal Logic

Metric LTL formulas rely on the next operator to encode time distances, whereas qualitative LTL formulas use only the until operator. This paper shows how to transform any metric LTL formula M into a qualitative formula Q, such that Q is satisfiable if and only if M is satisfiable over words with variability bounded with respect to the largest distances used in M (i.e., occurrences of next), but the size of Q is independent of such distances. Besides the theoretical interest, this result can help simplify the verification of systems with time-granularity heterogeneity, where large distances are required to express the coarse-grain dynamics in terms of fine-grain time units.Comment: Minor change

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

Time indeterminacy and spatio-temporal building transformations: an approach for architectural heritage understanding

Nowadays most digital reconstructions in architecture and archeology describe buildings heritage as awhole of static and unchangeable entities. However, historical sites can have a rich and complex history, sometimes full of evolutions, sometimes only partially known by means of documentary sources. Various aspects condition the analysis and the interpretation of cultural heritage. First of all, buildings are not inexorably constant in time: creation, destruction, union, division, annexation, partial demolition and change of function are the transformations that buildings can undergo over time. Moreover, other factors sometimes contradictory can condition the knowledge about an historical site, such as historical sources and uncertainty. On one hand, historical documentation concerning past states can be heterogeneous, dubious, incomplete and even contradictory. On the other hand, uncertainty is prevalent in cultural heritage in various forms: sometimes it is impossible to define the dating period, sometimes the building original shape or yet its spatial position. This paper proposes amodeling approach of the geometrical representation of buildings, taking into account the kind of transformations and the notion of temporal indetermination