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Amar Isli

Publications and source records attributed to Amar Isli.

10 recordsLinked to original sources
arXiv2020

A binarized-domains arc-consistency algorithm for TCSPs: its computational analysis and its use as a filtering procedure in solution search algorithms

TCSPs (Temporal Constraint Satisfaction Problems) [Dechter et al. 1991] get rid of unary constraints by binarizing them after having added an "origin of the world" variable. In this work, we look at the constraints between the "origin of the world" variable and the other variables, as the (binarized) domains of these other variables. With this in mind, we define a notion of arc-consistency for TCSPs, which we will refer to as binarized-domains Arc-Consistency, or bdArc-Consistency for short. We provide an algorithm achieving bdArc-Consistency for a TCSP, which we will refer to as bdAC-3, for it is an adaptation of Mackworth's [1977] well-known arc-consistency algorithm AC-3. We show that if an STP is bdArc-Consistent, and connected, i.e., its "origin of the world" variable is disconnected from none of the other variables, its binarized domains are minimal. We provide two polynomial backtrack-free procedures: one for the task of getting a solution from a connected bdArc-Consistent STP; the other for the task of getting, from a bdArc-Consistent STP, either that it is inconsistent or, in case of consistency, a connected bdArc-Consistent STP refinement. We then show how to use our results both in a general TCSP solver and in a TCSP-based job shop scheduler. The work also provides an experimental comparison on STPs of bdAC-3 with an existing arc-consistency algorithm, ACSTP, restricted to STPs [Kong et al. 2018]; an experimental comparison of three TCSP-based job shop schedulers, two of which use weak versions of bdAC-3 as the filtering procedure during the search, the third [Schwalb and Dechter 1997] a weak version of path-consistency; and the swi-prolog source codes used by these comparisons. Last but not least, we provide an incremental version of bdAC-3.

cs.AI↗
arXiv2020

Buchi automata augmented with spatial constraints: simulating an alternating with a nondeterministic and deciding the emptiness problem for the latter

The aim of this work is to thoroughly investigate Buchi automata augmented with spatial constraints. The input trees of such an automaton are infinite k-ary Sigma-trees, with the nodes standing for time points, and Sigma including, additionally to its uses in classical k-ary Sigma-trees, the description of the snapshot of an n-object spatial scene of interest. The constraints, from an RCC8-like spatial Relation Algebra (RA) x, are used to impose spatial constraints on objects of the spatial scene, eventually at different nodes of the input trees. We show that a Buchi alternating automaton augmented with spatial constraints can be simulated with a classical Buchi nondeterministic automaton of the same type, augmented with spatial constraints. We then provide a nondeterministic doubly depth-first polynomial space algorithm for the emptiness problem of the latter automaton. Our main motivation came from another work, also submitted to this conference, which defines a spatio-temporalisation of the well-known family ALC(D) of description logics with a concrete domain: together, the two works provide an effective solution to the satisfiability problem of a concept of the spatio-temporalisation with respect to a weakly cyclic TBox.

cs.FL↗
arXiv2020

A spatio-temporalisation of ALC(D) and its translation into alternating automata augmented with spatial constraints

The aim of this work is to provide a family of qualitative theories for spatial change in general, and for motion of spatial scenes in particular. To achieve this, we consider a spatio-temporalisation MTALC(Dx), of the well-known ALC(D) family of Description Logics (DLs) with a concrete domain: the MTALC(Dx) concepts are interpreted over infinite k-ary Sigma-trees, with the nodes standing for time points, and Sigma including, additionally to its uses in classical k-ary Sigma-trees, the description of the snapshot of an n-object spatial scene of interest; the roles split into m+n immediate-successor (accessibility) relations, which are serial, irreflexive and antisymmetric, and of which m are general, not necessarily functional, the other n functional; the concrete domain Dx is generated by an RCC8-like spatial Relation Algebra (RA) x, and is used to guide the change by imposing spatial constraints on objects of the "followed" spatial scene, eventually at different time points of the input trees. In order to capture the expressiveness of most modal temporal logics encountered in the literature, we introduce weakly cyclic Terminological Boxes (TBoxes) of MTALC(Dx), whose axioms capture the decreasing property of modal temporal operators. We show the important result that satisfiability of an MTALC(Dx) concept with respect to a weakly cyclic TBox can be reduced to the emptiness problem of a Buchi weak alternating automaton augmented with spatial constraints. In another work, complementary to this one, also submitted to this conference, we thoroughly investigate Buchi automata augmented with spatial constraints, and provide, in particular, a translation of an alternating into a nondeterministic, and an effective decision procedure for the emptiness problem of the latter.

cs.AI↗
arXiv2004

Integrating cardinal direction relations and other orientation relations in Qualitative Spatial Reasoning

We propose a calculus integrating two calculi well-known in Qualitative Spatial Reasoning (QSR): Frank's projection-based cardinal direction calculus, and a coarser version of Freksa's relative orientation calculus. An original constraint propagation procedure is presented, which implements the interaction between the two integrated calculi. The importance of taking into account the interaction is shown with a real example providing an inconsistent knowledge base, whose inconsistency (a) cannot be detected by reasoning separately about each of the two components of the knowledge, just because, taken separately, each is consistent, but (b) is detected by the proposed algorithm, thanks to the interaction knowledge propagated from each of the two compnents to the other.

cs.AI↗
arXiv2004

An ALC(D)-based combination of temporal constraints and spatial constraints suitable for continuous (spatial) change

We present a family of spatio-temporal theories suitable for continuous spatial change in general, and for continuous motion of spatial scenes in particular. The family is obtained by spatio-temporalising the well-known ALC(D) family of Description Logics (DLs) with a concrete domain D, as follows, where TCSPs denotes "Temporal Constraint Satisfaction Problems", a well-known constraint-based framework: (1) temporalisation of the roles, so that they consist of TCSP constraints (specifically, of an adaptation of TCSP constraints to interval variables); and (2) spatialisation of the concrete domain D: the concrete domain is now $D_x$, and is generated by a spatial Relation Algebra (RA) $x$, in the style of the Region-Connection Calculus RCC8. We assume durative truth (i.e., holding during a durative interval). We also assume the homogeneity property (if a truth holds during a given interval, it holds during all of its subintervals). Among other things, these assumptions raise the "conflicting" problem of overlapping truths, which the work solves with the use of a specific partition of the 13 atomic relations of Allen's interval algebra.

cs.AI↗
arXiv2003

Integrating existing cone-shaped and projection-based cardinal direction relations and a TCSP-like decidable generalisation

We consider the integration of existing cone-shaped and projection-based calculi of cardinal direction relations, well-known in QSR. The more general, integrating language we consider is based on convex constraints of the qualitative form $r(x,y)$, $r$ being a cone-shaped or projection-based cardinal direction atomic relation, or of the quantitative form $(α,β)(x,y)$, with $α,β\in [0,2π)$ and $(β-α)\in [0,π]$: the meaning of the quantitative constraint, in particular, is that point $x$ belongs to the (convex) cone-shaped area rooted at $y$, and bounded by angles $α$ and $β$. The general form of a constraint is a disjunction of the form $[r_1\vee...\vee r_{n_1}\vee (α_1,β_1)\vee...\vee (α_{n_2},β_{n_2})](x,y)$, with $r_i(x,y)$, $i=1... n_1$, and $(α_i,β_i)(x,y)$, $i=1... n_2$, being convex constraints as described above: the meaning of such a general constraint is that, for some $i=1... n_1$, $r_i(x,y)$ holds, or, for some $i=1... n_2$, $(α_i,β_i)(x,y)$ holds. A conjunction of such general constraints is a $\tcsp$-like CSP, which we will refer to as an $\scsp$ (Spatial Constraint Satisfaction Problem). An effective solution search algorithm for an $\scsp$ will be described, which uses (1) constraint propagation, based on a composition operation to be defined, as the filtering method during the search, and (2) the Simplex algorithm, guaranteeing completeness, at the leaves of the search tree. The approach is particularly suited for large-scale high-level vision, such as, e.g., satellite-like surveillance of a geographic area.

cs.AI↗
arXiv2003

A ternary Relation Algebra of directed lines

We define a ternary Relation Algebra (RA) of relative position relations on two-dimensional directed lines (d-lines for short). A d-line has two degrees of freedom (DFs): a rotational DF (RDF), and a translational DF (TDF). The representation of the RDF of a d-line will be handled by an RA of 2D orientations, CYC_t, known in the literature. A second algebra, TA_t, which will handle the TDF of a d-line, will be defined. The two algebras, CYC_t and TA_t, will constitute, respectively, the translational and the rotational components of the RA, PA_t, of relative position relations on d-lines: the PA_t atoms will consist of those pairs of a TA_t atom and a CYC_t atom that are compatible. We present in detail the RA PA_t, with its converse table, its rotation table and its composition tables. We show that a (polynomial) constraint propagation algorithm, known in the literature, is complete for a subset of PA_t relations including almost all of the atomic relations. We will discuss the application scope of the RA, which includes incidence geometry, GIS (Geographic Information Systems), shape representation, localisation in (multi-)robot navigation, and the representation of motion prepositions in NLP (Natural Language Processing). We then compare the RA to existing ones, such as an algebra for reasoning about rectangles parallel to the axes of an (orthogonal) coordinate system, a ``spatial Odyssey'' of Allen's interval algebra, and an algebra for reasoning about 2D segments.

cs.AI↗
arXiv2003

Bridging the gap between modal temporal logics and constraint-based QSR as an ALC(D) spatio-temporalisation with weakly cyclic TBoxes

The aim of this work is to provide a family of qualitative theories for spatial change in general, and for motion of spatial scenes in particular. To achieve this, we consider a spatio-temporalisation MTALC(D_x), of the well-known ALC(D) family of Description Logics (DLs) with a concrete domainan. In particular, the concrete domain D_x is generated by a qualitative spatial Relation Algebra (RA) x. We show the important result that satisfiability of an MTALC(D_x) concept with respect to a weakly cyclic TBox is decidable in nondeterministic exponential time, by reducing it to the emptiness problem of a weak alternating automaton augmented with spatial constraints, which we show to remain decidable, although the accepting condition of a run involves, additionally to the standard case, consistency of a CSP (Constraint Satisfaction Problem) potentially infinite. The result provides an effective tableaux-like satisfiability procedure which is discussed.

cs.AI↗