1,450 research outputs found
Combining Spatial and Temporal Logics: Expressiveness vs. Complexity
In this paper, we construct and investigate a hierarchy of spatio-temporal
formalisms that result from various combinations of propositional spatial and
temporal logics such as the propositional temporal logic PTL, the spatial
logics RCC-8, BRCC-8, S4u and their fragments. The obtained results give a
clear picture of the trade-off between expressiveness and computational
realisability within the hierarchy. We demonstrate how different combining
principles as well as spatial and temporal primitives can produce NP-, PSPACE-,
EXPSPACE-, 2EXPSPACE-complete, and even undecidable spatio-temporal logics out
of components that are at most NP- or PSPACE-complete
A Modal Logic for Subject-Oriented Spatial Reasoning
We present a modal logic for representing and reasoning about space seen from the subject\u27s perspective. The language of our logic comprises modal operators for the relations "in front", "behind", "to the left", and "to the right" of the subject, which introduce the intrinsic frame of reference; and operators for "behind an object", "between the subject and an object", "to the left of an object", and "to the right of an object", employing the relative frame of reference. The language allows us to express nominals, hybrid operators, and a restricted form of distance operators which, as we demonstrate by example, makes the logic interesting for potential applications. We prove that the satisfiability problem in the logic is decidable and in particular PSpace-complete
Modal Logics of Topological Relations
Logical formalisms for reasoning about relations between spatial regions play
a fundamental role in geographical information systems, spatial and constraint
databases, and spatial reasoning in AI. In analogy with Halpern and Shoham's
modal logic of time intervals based on the Allen relations, we introduce a
family of modal logics equipped with eight modal operators that are interpreted
by the Egenhofer-Franzosa (or RCC8) relations between regions in topological
spaces such as the real plane. We investigate the expressive power and
computational complexity of logics obtained in this way. It turns out that our
modal logics have the same expressive power as the two-variable fragment of
first-order logic, but are exponentially less succinct. The complexity ranges
from (undecidable and) recursively enumerable to highly undecidable, where the
recursively enumerable logics are obtained by considering substructures of
structures induced by topological spaces. As our undecidability results also
capture logics based on the real line, they improve upon undecidability results
for interval temporal logics by Halpern and Shoham. We also analyze modal
logics based on the five RCC5 relations, with similar results regarding the
expressive power, but weaker results regarding the complexity
Temporal Data Modeling and Reasoning for Information Systems
Temporal knowledge representation and reasoning is a major research field in Artificial
Intelligence, in Database Systems, and in Web and Semantic Web research. The ability to
model and process time and calendar data is essential for many applications like appointment
scheduling, planning, Web services, temporal and active database systems, adaptive
Web applications, and mobile computing applications. This article aims at three complementary
goals. First, to provide with a general background in temporal data modeling
and reasoning approaches. Second, to serve as an orientation guide for further specific
reading. Third, to point to new application fields and research perspectives on temporal
knowledge representation and reasoning in the Web and Semantic Web
Answer Set Programming Modulo `Space-Time'
We present ASP Modulo `Space-Time', a declarative representational and
computational framework to perform commonsense reasoning about regions with
both spatial and temporal components. Supported are capabilities for mixed
qualitative-quantitative reasoning, consistency checking, and inferring
compositions of space-time relations; these capabilities combine and synergise
for applications in a range of AI application areas where the processing and
interpretation of spatio-temporal data is crucial. The framework and resulting
system is the only general KR-based method for declaratively reasoning about
the dynamics of `space-time' regions as first-class objects. We present an
empirical evaluation (with scalability and robustness results), and include
diverse application examples involving interpretation and control tasks
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
Horn fragments of the Halpern-Shoham Interval Temporal Logic
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
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