A complete reified temporal logic and its applications

Temporal representation and reasoning plays a fundamental and increasingly important role in some areas of Computer Science and Artificial Intelligence. A natural approach to represent and reason about time-dependent knowledge is to associate them with instantaneous time points and/or durative time intervals. In particular, there are various ways to use logic formalisms for temporal knowledge representation and reasoning. Based on the chosen logic frameworks, temporal theories can be classified into modal logic approaches (including prepositional modal logic approaches and hybrid logic approaches) and predicate logic approaches (including temporal argument methods and temporal reification methods). Generally speaking, the predicate logic approaches are more expressive than the modal logic approaches and among predicate logic approaches, temporal reification methods are even more expressive for representing and reasoning about general temporal knowledge. However, the current reified temporal logics are so complicate that each of them either do not have a clear definition of its syntax and semantics or do not have a sound and complete axiomatization. In this thesis, a new complete reified temporal logic (CRTL) is introduced which has a clear syntax, semantics, and a complete axiomatic system by inheriting from the initial first order language. This is the main improvement made to the reification approaches for temporal representation and reasoning. It is a true reified logic since some meta-predicates are formally defined that allow one to predicate and quantify over prepositional terms, and therefore provides the expressive power to represent and reason about both temporal and non-temporal relationships between prepositional terms. For a special case, the temporal model of the simplified CRTL system (SCRTL) is defined as scenarios and graphically represented in terms of a directed, partially weighted or attributed, simple graph. Therefore, the problem of matching temporal scenarios is transformed into conventional graph matching. For the scenario graph matching problem, the traditional eigen-decomposition graph matching algorithm and the symmetric polynomial transform graph matching algorithm are critically examined and improved as two new algorithms named meta-basis graph matching algorithm and sort based graph matching algorithm respectively, where the meta-basis graph matching algorithm works better for 0-1 matrices while the sort based graph matching algorithm is more suitable for continuous real matrices. Another important contribution is the node similarity graph matching framework proposed in this thesis, based on which the node similarity graph matching algorithms can be defined, analyzed and extended uniformly. We prove that that all these node similarity graph matching algorithms fail to work for matching circles

A cookbook for temporal conceptual data modelling with description logic

We design temporal description logics suitable for reasoning about temporal conceptual data models and investigate their computational complexity. Our formalisms are based on DL-Lite logics with three types of concept inclusions (ranging from atomic concept inclusions and disjointness to the full Booleans), as well as cardinality constraints and role inclusions. In the temporal dimension, they capture future and past temporal operators on concepts, flexible and rigid roles, the operators `always' and `some time' on roles, data assertions for particular moments of time and global concept inclusions. The logics are interpreted over the Cartesian products of object domains and the flow of time (Z,<), satisfying the constant domain assumption. We prove that the most expressive of our temporal description logics (which can capture lifespan cardinalities and either qualitative or quantitative evolution constraints) turn out to be undecidable. However, by omitting some of the temporal operators on concepts/roles or by restricting the form of concept inclusions we obtain logics whose complexity ranges between PSpace and NLogSpace. These positive results were obtained by reduction to various clausal fragments of propositional temporal logic, which opens a way to employ propositional or first-order temporal provers for reasoning about temporal data models

A Temporal extension of Prolog

AbstractTemporal Prolog, a temporal logic extension of PROLOG, is presented. The primary criterion for the model selection has been its natural embedment into the logic programming paradigm. Under strong efficiency constraints, a first-order “reified” logic has been taken as a basis for the implementation. Allen's temporal constraint algorithm has been extended for treatment of retractable constraints. Their embedment into Temporal Prolog can be viewed as an instance of the Constraint Logic Programming paradigm. An example inspired by K. Forbus's Qualitative Process Theory illustrates how qualitative simulation and related tasks can be formulated in Temporal Prolog in a transparent and declarative way

Clafer: Lightweight Modeling of Structure, Behaviour, and Variability

Embedded software is growing fast in size and complexity, leading to intimate mixture of complex architectures and complex control. Consequently, software specification requires modeling both structures and behaviour of systems. Unfortunately, existing languages do not integrate these aspects well, usually prioritizing one of them. It is common to develop a separate language for each of these facets. In this paper, we contribute Clafer: a small language that attempts to tackle this challenge. It combines rich structural modeling with state of the art behavioural formalisms. We are not aware of any other modeling language that seamlessly combines these facets common to system and software modeling. We show how Clafer, in a single unified syntax and semantics, allows capturing feature models (variability), component models, discrete control models (automata) and variability encompassing all these aspects. The language is built on top of first order logic with quantifiers over basic entities (for modeling structures) combined with linear temporal logic (for modeling behaviour). On top of this semantic foundation we build a simple but expressive syntax, enriched with carefully selected syntactic expansions that cover hierarchical modeling, associations, automata, scenarios, and Dwyer's property patterns. We evaluate Clafer using a power window case study, and comparing it against other notations that substantially overlap with its scope (SysML, AADL, Temporal OCL and Live Sequence Charts), discussing benefits and perils of using a single notation for the purpose

Towards an Aesthetics of the (in)formel: Time, Space and the Dialectical Image in the Music of Varèse, Feldman and Xenakis

This thesis addresses the issue of the modernist musical artwork, specifically in terms of the spatialization of musical time, in aesthetic and music-analytic terms. Firstly, it focuses on the notion of musique informelle as it was expounded in Adorno’s essay ‘Vers une musique informelle,’ (1961) and its place in Gianmario Borio’s elaboration of this in terms of an aesthetics of the informel. Secondly, it proposes a further expansion of these aesthetics via a double strategy: a comparative reading of Walter Benjamin’s critique of philosophies of time (including the work of Henri Bergson), language and objects, and furthermore a reconceptualization of both Adorno’s and Borio’s aesthetics in terms of a new theory of the object (as sound-object) in light of a new reading strategy. This reading is based on Walter Benjamin’s notion of the dialectical image, which proposes a new form of philosophical interpretation. The theorizations of the sound-object and the dialectical image furnish a basis for a re-conceptalization of the (in)formel, allowing for the interpretative reading of the music of three composers in particular: Edgard Varèse, Morton Feldman and Iannis Xenakis. Particularly, the study of a number of their works, including Intégrales (Varèse), On Time and the Instrumental Factor and Words and Music (Feldman), and Duel (Xenakis), reveals what Adorno terms their (truth) content, in their mediation of rationalization and intuition. Finally, it is argued that these modernist works can in turn bring new insights into Adorno’s aesthetics of the modernist work of art

Industrialism and the fragmentation of temporal structure

Industrialism's assimilation of the natural world has developed over centuries through complex hierarchies of effects involving ecological, cultural and psychological dimensions. One of the consequences of this assimilation, I argue, is the fragmentation of the temporal structure of the world, and its replacement by a short-term logic that also infects human subjectivity. Because of this fragmentation, the healing of the natural world cannot be realised either simply or directly, and effective action will require us to locate our immediate objectives within a recovered longer-term vision of a healthy natural world

ESSENTIAL PROPERTIES OF LANGUAGE FROM THE POINT OF VIEW OF AUTOPOIESIS

The structuralist heritage in linguistics continues to obscure the essential properties of natural language as an empirical phenomenon. It is argued that the new framework of autopoiesis possesses a greater explanatory power, as it assumes the connotational na-ture of language. The key notions of representation, sign and signification, interpreta-tion, intentionality and communication, and reciprocal causality, approached from the autopoietic angle, allow for deeper insights into the essence of language which is as a kind of adaptive behavior of an organism involving a system constituted by signs of signs