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

Computational Complexity of a Core Fragment of Halpern-Shoham Logic

Halpern-Shoham logic (HS) is a highly expressive interval temporal logic but the satisfiability problem of its formulas is undecidable. The main goal in the research area is to introduce fragments of the logic which are of low computational complexity and of expressive power high enough for practical applications. Recently introduced syntactical restrictions imposed on formulas and semantical constraints put on models gave rise to tractable HS fragments for which prototypical real-world applications have already been proposed. One of such fragments is obtained by forbidding diamond modal operators and limiting formulas to the core form, i.e., the Horn form with at most one literal in the antecedent. The fragment was known to be NL-hard and in P but no tight results were known. In the paper we prove its P-completeness in the case where punctual intervals are allowed and the timeline is dense. Importantly, the fragment is not referential, i.e., it does not allow us to express nominals (which label intervals) and satisfaction operators (which enables us to refer to intervals by their labels). We show that by adding nominals and satisfaction operators to the fragment we reach NP-completeness whenever the timeline is dense or the interpretation of modal operators is weakened (excluding the case when punctual intervals are disallowed and the timeline is discrete). Moreover, we prove that in the case of language containing nominals but not satisfaction operators, the fragment is still NP-complete over dense timelines

On Expressiveness of Halpern-Shoham Logic and its Horn Fragments

Abstract: Halpern and Shoham\u27s modal logic of time intervals (HS in short) is an elegant and highly influential propositional interval-based logic. Its Horn fragments and their hybrid extensions have been recently intensively studied and successfully applied in real-world use cases. Detailed investigation of their decidability and computational complexity has been conducted, however, there has been significantly less research on their expressive power. In this paper we make a step towards filling this gap. We (1) show what time structures are definable in the language of HS, and (2) determine which HS fragments are capable of expressing: hybrid machinery, i.e., nominals and satisfaction operators, and somewhere, difference, and everywhere modal operators. These results enable us to classify HS Horn fragments according to their expressive power and to gain insight in the interplay between their decidability/computational complexity and expressiveness

Testing the Temporal Limits of Lures and Toxicants for Trapping Fruit Flies (Diptera: Tephritidae): Additional Weathering Studies of Solid Bactrocera and Zeugodacus Male Lures and Associated Insecticidal Strips

Detection of pestiferous fruit flies (Diptera: Tephritidae) relies largely on traps baited with male-specific attractants. Surveillance programs in Florida and California use liquid methyl eugenol (ME, attractive to males of Bactrocera dorsalis (Hendel)) and liquid cue-lure (CL, attractive to males of Zeugodacus cucurbitae (Coquillett)) mixed with the toxicant naled to bait detection traps. However, this practice requires considerable time and may subject personnel to health risks. Recent work indicates that solid male lures deployed with a separate insecticidal (DDVP) strip are as effective as the standard liquid formulations. Specifically, solid ME and CL dispensers and DDVP strips were weathered for 6 or 12 weeks under summer conditions in AZ and FL and subsequently field tested in Hawaii. Results showed that (i) solid ME dispensers weathered for 6 weeks, but not 12 weeks, were as attractive as fresh liquid ME, and (ii) solid CL dispensers and the insecticidal strips were as effective as fresh liquid formulation for at least 12 weeks. The present study expands upon these earlier findings and addresses two specific questions: Could solid ME dispensers be deployed for 8 or 10 weeks without loss of effectiveness? Could solid CL dispensers and insecticidal strips be deployed for intervals even longer than 12 weeks? Adopting the same protocol noted above, the present study indicates that effective field longevities are 10 weeks for solid ME dispensers, at least 20 weeks for solid CL dispensers, and 12 weeks for the DDVP strips. Comparisons are drawn with related studies, and implications for tephritid surveillance programs are discussed

Temporal datalog with existential quantification

Existential rules, also known as tuple-generating dependencies (TGDs) or Datalog± rules, are heavily studied in the communities of Knowledge Representation and Reasoning, Semantic Web, and Databases, due to their rich modelling capabilities. In this paper we consider TGDs in the temporal setting, by introducing and studying DatalogMTL∃—an extension of metric temporal Datalog (DatalogMTL) obtained by allowing for existential rules in programs. We show that DatalogMTL∃ is undecidable even in the restricted cases of guarded and weakly-acyclic programs. To address this issue we introduce uniform semantics which, on the one hand, is well-suited for modelling temporal knowledge as it prevents from unintended value invention and, on the other hand, provides decidability of reasoning; in particular, it becomes 2-ExpSpace-complete for weakly-acyclic programs but remains undecidable for guarded programs. We provide an implementation for the decidable case and demonstrate its practical feasibility. Thus we obtain an expressive, yet decidable, rule-language and a system which is suitable for complex temporal reasoning with existential rules