14 research outputs found
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
Computational Complexity of Strong Admissibility for Abstract Dialectical Frameworks
Abstract dialectical frameworks (ADFs) have been introduced as a formalism for modeling and evaluating argumentation allowing general logical satisfaction conditions. Different criteria used to settle the acceptance of arguments arecalled semantics. Semantics of ADFs have so far mainly been defined based on the concept of admissibility. Recently, the notion of strong admissibility has been introduced for ADFs. In the current work we study the computational complexityof the following reasoning tasks under strong admissibility semantics. We address 1. the credulous/skeptical decision problem; 2. the verification problem; 3. the strong justification problem; and 4. the problem of finding a smallest witness of strong justification of a queried argument
Feyerabend and incommensurability
I consider only the semantic claims of Paul Feyerabend's incommensurability thesis. These semantic claims are that incommensurable scientific theories, taken paradigmatically as successive theories: (1) are inconsistent; (2) the terms of one theory differ in meaning to those of another incommensurable theory; and (3) the claims of one theory are largely logically independent of the other. Since the inconsistency claim (1) is essential to Feyerabend's argument (against the Received View on theory reduction and explanation), I claim that (2) and (3) must be understood in the light of (1), and that (3) must be revised to avoid contradiction with (1). Feyerabend's semantic theory supporting (3) is presented and found wanting. Two other main arguments against (3) are also considered. The first is the causal theory of reference (of Putnam and Devitt), including causal descriptive theories advocated by Kitcher and Psillos; none of these theories is found to offer compelling reasons to reject (3). The second main argument against (3) is Donald Davidson's essay 'On the Very Idea of a Conceptual Scheme', and a close reading of Davidson's paper is offered. I find that Davidson does offer convincing reasons for rejecting any implication by (3) that the languages of incommensurable theories are not intertranslatable, or that such theories are closed cognitive frameworks. However, I agree with Larry Laudan that Davidson does not deliver a fatal blow to the semantic incommensurabihty thesis because: (a) incommensurability need not entail nontranslatability; and (b) Davidson's semantic arguments do not succeed in demonstrating that the very notion of a conceptual scheme is incoherent. I present briefly two versions of the semantic incommensurability thesis which are consistent in an interesting way with (1), (2) and a revised (3), namely taxonomic incommensurability and a model of misinterpretation in intractable conflicts
Logical tools for handling change in agent-based systems
We give a unified approach to various results and problems of nonclassical
logic