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An interval temporal logic is a propositional, multi-modal logic interpreted over interval structures of partial orders. The semantics of each modal operator are given in the standard way with respect to one of the natural accessibility relations defined on such interval structures. In this paper, we consider the modal operators based on the (reflexive) sub-interval relation and the (reflexive) super-interval...
Temporal reasoning plays an important role in artificial intelligence. Temporal logics provide a natural framework for its formalization and implementation. A standard way of enhancing the expressive power of temporal logics is to replace their unidimensional domain by a multidimensional one. In particular, such a dimensional increase can be exploited to obtain spatial counterparts of temporal logics...
Let M be an n?? ?? n matrix of rank r ?? n, and assume that a uniformly random subset E of its entries is observed. We describe an efficient algorithm that reconstructs M from |E| = O(r n) observed entries with relative root mean square error RMSE ?? C(??) (nr/|E|)1/2. Further, if r = O(1) and M is sufficiently unstructured, then it can be reconstructed exactly from |E| = O(n log n) entries. This...
How many random entries of an n times nalpha, rank r matrix are necessary to reconstruct the matrix within an accuracy delta? We address this question in the case of a random matrix with bounded rank, whereby the observed entries are chosen uniformly at random. We prove that, for any delta Gt 0, C(r, delta)n observations are sufficient. Finally we discuss the question of reconstructing the matrix...
Propositional interval temporal logics come into play in many areas of artificial intelligence and computer science. Unfortunately, most of them turned out to be (highly) undecidable. Some positive exceptions, belonging to the classes of neighborhood logics and of logics of subinterval relations, have been recently identified. In this paper, we address the decision problem for the future fragment...
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