PSPACE Reasoning for Graded Modal Logics

We present a PSPACE algorithm that decides satisfiability of the graded modal logic Gr(K_R)---a natural extension of propositional modal logic K_R by counting expressions---which plays an important role in the area of knowledge representation. The algorithm employs a tableaux approach and is the first known algorithm which meets the lower bound for the complexity of the problem. Thus, we exactly fix the complexity of the problem and refute an ExpTime-hardness conjecture. We extend the results to the logic Gr(K_(R \cap I)), which augments Gr(K_R) with inverse relations and intersection of accessibility relations. This establishes a kind of ``theoretical benchmark'' that all algorithmic approaches can be measured against

Context Aware Textual Entailment

In conversations, stories, news reporting, and other forms of natural language, understanding requires participants to make assumptions (hypothesis) based on background knowledge, a process called entailment. These assumptions may then be supported, contradicted, or refined as a conversation or story progresses and additional facts become known and context changes. It is often the case that we do not know an aspect of the story with certainty but rather believe it to be the case; i.e., what we know is associated with uncertainty or ambiguity. In this research a method has been developed to identify different contexts of the input raw text along with specific features of the contexts such as time, location, and objects. The method includes a two-phase SVM classifier along with a voting mechanism in the second phase to identify the contexts. Rule-based algorithms were utilized to extract the context elements. This research also develops a new context˗aware text representation. This representation maintains semantic aspects of sentences, as well as textual contexts and context elements. The method can offer both graph representation and First-Order-Logic representation of the text. This research also extracts a First-Order Logic (FOL) and XML representation of a text or series of texts. The method includes entailment using background knowledge from sources (VerbOcean and WordNet), with resolution of conflicts between extracted clauses, and handling the role of context in resolving uncertain truth

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

Presence-at-hand

Abstract The writing that follows is intended to provide a theoretical framework for the motives behind my practice. The primary concerns addressed are the reception, transmission, and physical shape of knowledge. I will discuss a human condition that exists as a byproduct of both the legacy of representation as well as the innate biology of the brain. I will argue that as a society we are governed by the residue of an extreme logic, and that this condition places severe margins on our potential for creative solutions. I will propose that our ability to create meaning is stifled by the nature of representation itself—and that the overwhelming presence of logic in the mind fosters an unfavorable environment for radical ideas to occur. Through focusing on the limitations of language and habits of the mind topics will explore my work, and the role of art, as a site for the emergence of an unconventional kind of relearning

A declarative integration of terminological, constraint-based, data-driven, and goal-directed reasoning

The paper settles a research branch in the realm of logic-oriented, hybrid knowledge representation. Terminological knowledge representation and reasoning can now be utilized for more realistic applications as an integral component of a computationally complete, declarative hybrid knowledge representation formalism with integrated special-purpose reasoners of concrete domains such as real-closed fields or finite-domain constraints. The paper presents technical results exploring the impact of "role interaction" on the decidability of the subsumption problem of terminological logics. In particular, decision procedures are presented for common reasoning problems in an expressive terminological logic that is parametrized by a concrete domain. A refined minimal belief logic which avoids certain problems concerning the non-propositional case (which ocurred surprisingly) is the basis of the model-theoretic semantics of a very general generic rule formalism integrating goal-directed (i.e., top-down) and data-driven (i.e., bottom-up) reasoning in a declarative manner. A mechanical engineering application (production planning of lathes) is used to demonstrate how the theoretical results can be employed in realistic applications

On the Existence of Characterization Logics and Fundamental Properties of Argumentation Semantics

Given the large variety of existing logical formalisms it is of utmost importance to select the most adequate one for a specific purpose, e.g. for representing the knowledge relevant for a particular application or for using the formalism as a modeling tool for problem solving. Awareness of the nature of a logical formalism, in other words, of its fundamental intrinsic properties, is indispensable and provides the basis of an informed choice. One such intrinsic property of logic-based knowledge representation languages is the context-dependency of pieces of knowledge. In classical propositional logic, for example, there is no such context-dependence: whenever two sets of formulas are equivalent in the sense of having the same models (ordinary equivalence), then they are mutually replaceable in arbitrary contexts (strong equivalence). However, a large number of commonly used formalisms are not like classical logic which leads to a series of interesting developments. It turned out that sometimes, to characterize strong equivalence in formalism L, we can use ordinary equivalence in formalism L0: for example, strong equivalence in normal logic programs under stable models can be characterized by the standard semantics of the logic of here-and-there. Such results about the existence of characterizing logics has rightly been recognized as important for the study of concrete knowledge representation formalisms and raise a fundamental question: Does every formalism have one? In this thesis, we answer this question with a qualified “yes”. More precisely, we show that the important case of considering only finite knowledge bases guarantees the existence of a canonical characterizing formalism. Furthermore, we argue that those characterizing formalisms can be seen as classical, monotonic logics which are uniquely determined (up to isomorphism) regarding their model theory. The other main part of this thesis is devoted to argumentation semantics which play the flagship role in Dung’s abstract argumentation theory. Almost all of them are motivated by an easily understandable intuition of what should be acceptable in the light of conflicts. However, although these intuitions equip us with short and comprehensible formal definitions it turned out that their intrinsic properties such as existence and uniqueness, expressibility, replaceability and verifiability are not that easily accessible. We review the mentioned properties for almost all semantics available in the literature. In doing so we include two main axes: namely first, the distinction between extension-based and labelling-based versions and secondly, the distinction of different kind of argumentation frameworks such as finite or unrestricted ones