Papers by Emilio Jose Muñoz Velasco
The primary characteristic of interval temporal logic is that intervals, rather than points, are ... more The primary characteristic of interval temporal logic is that intervals, rather than points, are taken as the primitive ontological entities. Given their generally bad computational behavior of interval temporal logics, several techniques exist to produce decidable and computationally affordable temporal logics based on intervals. In this paper we take inspiration from Golumbic and Shamir's coarser interval algebras, which generalize the classical Allen's Interval Algebra, in order to define two previously unknown variants of Halpern and Shoham's logic (HS) based on coarser relations. We prove that, perhaps surprisingly, the satisfiability problem for the coarsest of the two variants, namely HS 3 , not only is decidable, but PSpace-complete in the finite/discrete case, and PSpace-hard in any other case; besides proving its complexity bounds, we implement a tableau-based satisfiability checker for it and test it against a systematically generated benchmark. Our results are strengthened by showing that not all coarser-than-Allen's relations are a guarantee of decidability, as we prove that the second variant, namely HS 7 , remains undecidable in all interesting cases.
We present a logic approach to reason with moving objects under fuzzy qualitative representation.... more We present a logic approach to reason with moving objects under fuzzy qualitative representation. This way, we can deal both with qualitative and quantitative information, and consequently, to obtain more accurate results. The proposed logic system is introduced as an extension of Propositional Dynamic Logic: this choice, on the one hand, simplifies the theoretical study concerning soundness, completeness and decidability; on the other hand, provides the possibility of constructing complex relations from simpler ones and the use of a language very close to programming languages.
In this paper, we consider the well-known modal logics K, T, K4, and S4, and we study some of the... more In this paper, we consider the well-known modal logics K, T, K4, and S4, and we study some of their sub-propositional fragments, namely the classical Horn fragment, the Krom fragment, the so-called core fragment, defined as the intersection of the Horn and the Krom fragments, plus their sub-fragments obtained by limiting the use of boxes and diamonds in clauses. We focus, first, on the relative expressive power of such languages: we introduce a suitable measure of expressive power, and we obtain a complex hierarchy that encompasses all fragments of the considered logics. Then, after observing the low expressive power, in particular, of the Horn fragments without diamonds, we study the computational complexity of their satisfiability problem, proving that, in general, it becomes polynomial.
We introduce a multimodal logic for order of magnitude reasoning which considers a new logic-base... more We introduce a multimodal logic for order of magnitude reasoning which considers a new logic-based alternative to the notion of closeness, we provide an axiom system and prove its soundness and completeness.
Discovering association rules is a classical data mining task with a wide range of applications t... more Discovering association rules is a classical data mining task with a wide range of applications that include the medical, the financial, and the planning domains, among others. Modern rule extraction algorithms focus on static rules, typically expressed in the language of Horn propos-itional logic, as opposed to temporal ones, which have received less attention in the literature. Since in many application domains temporal information is stored in form of intervals, extracting interval-based temporal rules seems the natural choice. In this paper we extend the well-known algorithm APRIORI for rule extraction to discover interval temporal rules written in the Horn fragment of Halpern and Shoham's interval temporal logic.
In this paper, we focus on a logical approach to the important notion of closeness, which has not... more In this paper, we focus on a logical approach to the important notion of closeness, which has not received much attention in the literature. Our notion of closeness is based on the so-called proximity intervals , which will be used to decide the elements that are close to each other. Some of the intuitions of this definition are explained on the basis of examples. We prove the decidability of the recently introduced mul-timodal logic for closeness and, then, we show some capabilities of the logic with respect to expressivity in order to denote particular positions of the proximity intervals.
We investigate the satisfiability problem for Horn fragments of the Halpern-Shoham interval tempo... more We investigate the satisfiability problem for Horn fragments of the Halpern-Shoham interval temporal logic depending on the type (box or diamond) of the interval modal operators, the type of the underlying linear order (discrete or dense), and the type of semantics for the interval relations (reflexive or irreflexive). For example, we show that satisfiability of Horn formulas with diamonds is undecidable for any type of linear orders and semantics. On the contrary, satisfiability of Horn formulas with boxes is tractable over both discrete and dense orders under the reflexive semantics and over dense orders under the irreflexive semantics, but becomes undecidable over discrete orders under the irreflexive semantics. Satisfiability of binary Horn formulas with both boxes and diamonds is always undecidable under the irreflexive semantics.
The chop operator C is a binary modality that plays an important role in interval temporal logics... more The chop operator C is a binary modality that plays an important role in interval temporal logics. Such an operator, which is not definable in Halpern and Shoham's modal logic of time intervals HS, allows one to split an interval into two parts and to specify what is true over them. The modality C appears in Moszkowski's PITL (that includes C plus a modal constant π that is true on intervals with coincident endpoints only) and in Venema's CDT (which features, besides C, the binary modalities D and T , and π). Without the so-called locality principle, which restricts the semantics of propositions, the satisfiability problem of both these logics is undecidable when interpreted in any meaningful class of linearly ordered sets, and, recently, it has been proven that such a result still holds over infinite linear orders in the fragment C; this leaves as open the status of the satisfiability problem of C, that is, PITL without π, in the finite case. To solve it, we take advantage from the close relation between C and the reflexive version of the HS-fragments BE HS (with modalities corresponding to Allen's relations starts and finishes) and D HS (during); we know that the latter is decidable in PSPACE in the finite case, while the status of the satisfiability problem of the former is unknown. In this paper we prove that the satisfiability problem for BE HS is undecidable, and the undecidability of the same problem for C comes as a corollary.
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Papers by Emilio Jose Muñoz Velasco