Towards More Useful Description Logics of Time, Change and Context

Description Logics (DLs) are a family of logic-based formalisms for the representation of and reasoning about knowledge. Classical DLs are fragments of first-order logic and therefore aim at capturing static knowledge. Alas, the lack of means of DLs to capture dynamic aspects of knowledge has been often criticized because many important DL applications depend on this kind of knowledge. As a reaction to this shortcoming of DLs, two-dimensional extensions of DLs with capabilities to represent and reason about dynamic knowledge were introduced. We further, in this thesis, the understanding and utility of two-dimensional DLs. We particularly focus on identifying two-dimensional DLs providing the right expressive power to model more accurately temporal and contextual aspects of knowledge required by certain DL applications, or providing better computational properties than other possible alternatives. We pursue three lines of research: we study branching-time temporal DLs that emerge from the combination of classical DLs with the classical temporal logics CTL* and CTL; we study description logics of change that emerge from the combination of classical DLs with the modal logic S5; we study description logics of context that emerge from the combination of classical DLs with multi-modal logics. We investigate temporal and contextual DLs based on the classical DL ALC and on members of the EL-family of DLs. Our main technical contributions are algorithms for satisfiability and subsumption, and (mostly) tight complexity bounds

Towards More Useful Description Logics of Time, Change and Context

Description Logics (DLs) are a family of logic-based formalisms for the representation of and reasoning about knowledge. Classical DLs are fragments of first-order logic and therefore aim at capturing static knowledge. Alas, the lack of means of DLs to capture dynamic aspects of knowledge has been often criticized because many important DL applications depend on this kind of knowledge. As a reaction to this shortcoming of DLs, two-dimensional extensions of DLs with capabilities to represent and reason about dynamic knowledge were introduced. We further, in this thesis, the understanding and utility of two-dimensional DLs. We particularly focus on identifying two-dimensional DLs providing the right expressive power to model more accurately temporal and contextual aspects of knowledge required by certain DL applications, or providing better computational properties than other possible alternatives. We pursue three lines of research: we study branching-time temporal DLs that emerge from the combination of classical DLs with the classical temporal logics CTL* and CTL; we study description logics of change that emerge from the combination of classical DLs with the modal logic S5; we study description logics of context that emerge from the combination of classical DLs with multi-modal logics. We investigate temporal and contextual DLs based on the classical DL ALC and on members of the EL-family of DLs. Our main technical contributions are algorithms for satisfiability and subsumption, and (mostly) tight complexity bounds

Neurons and symbols: a manifesto

We discuss the purpose of neural-symbolic integration including its principles, mechanisms and applications. We outline a cognitive computational model for neural-symbolic integration, position the model in the broader context of multi-agent systems, machine learning and automated reasoning, and list some of the challenges for the area of neural-symbolic computation to achieve the promise of effective integration of robust learning and expressive reasoning under uncertainty

Logic-Based Specification Languages for Intelligent Software Agents

The research field of Agent-Oriented Software Engineering (AOSE) aims to find abstractions, languages, methodologies and toolkits for modeling, verifying, validating and prototyping complex applications conceptualized as Multiagent Systems (MASs). A very lively research sub-field studies how formal methods can be used for AOSE. This paper presents a detailed survey of six logic-based executable agent specification languages that have been chosen for their potential to be integrated in our ARPEGGIO project, an open framework for specifying and prototyping a MAS. The six languages are ConGoLog, Agent-0, the IMPACT agent programming language, DyLog, Concurrent METATEM and Ehhf. For each executable language, the logic foundations are described and an example of use is shown. A comparison of the six languages and a survey of similar approaches complete the paper, together with considerations of the advantages of using logic-based languages in MAS modeling and prototyping.Comment: 67 pages, 1 table, 1 figure. Accepted for publication by the Journal "Theory and Practice of Logic Programming", volume 4, Maurice Bruynooghe Editor-in-Chie

State-of-the-art on evolution and reactivity

This report starts by, in Chapter 1, outlining aspects of querying and updating resources on the Web and on the Semantic Web, including the development of query and update languages to be carried out within the Rewerse project. From this outline, it becomes clear that several existing research areas and topics are of interest for this work in Rewerse. In the remainder of this report we further present state of the art surveys in a selection of such areas and topics. More precisely: in Chapter 2 we give an overview of logics for reasoning about state change and updates; Chapter 3 is devoted to briefly describing existing update languages for the Web, and also for updating logic programs; in Chapter 4 event-condition-action rules, both in the context of active database systems and in the context of semistructured data, are surveyed; in Chapter 5 we give an overview of some relevant rule-based agents frameworks

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 first-order Temporal Logic for Actions

We present a multi-modal action logic with first-order modalities, which contain terms which can be unified with the terms inside the subsequent formulas and which can be quantified. This makes it possible to handle simultaneously time and states. We discuss applications of this language to action theory where it is possible to express many temporal aspects of actions, as for example, beginning, end, time points, delayed preconditions and results, duration and many others. We present tableaux rules for a decidable fragment of this logic

Counterpart semantics for a second-order mu-calculus

We propose a novel approach to the semantics of quantified μ-calculi, considering models where states are algebras; the evolution relation is given by a counterpart relation (a family of partial homomorphisms), allowing for the creation, deletion, and merging of components; and formulas are interpreted over sets of state assignments (families of substitutions, associating formula variables to state components). Our proposal avoids the limitations of existing approaches, usually enforcing restrictions of the evolution relation: the resulting semantics is a streamlined and intuitively appealing one, yet it is general enough to cover most of the alternative proposals we are aware of