1,693 research outputs found
Generating Schemata of Resolution Proofs
Two distinct algorithms are presented to extract (schemata of) resolution
proofs from closed tableaux for propositional schemata. The first one handles
the most efficient version of the tableau calculus but generates very complex
derivations (denoted by rather elaborate rewrite systems). The second one has
the advantage that much simpler systems can be obtained, however the considered
proof procedure is less efficient
Correspondences between Classical, Intuitionistic and Uniform Provability
Based on an analysis of the inference rules used, we provide a
characterization of the situations in which classical provability entails
intuitionistic provability. We then examine the relationship of these
derivability notions to uniform provability, a restriction of intuitionistic
provability that embodies a special form of goal-directedness. We determine,
first, the circumstances in which the former relations imply the latter. Using
this result, we identify the richest versions of the so-called abstract logic
programming languages in classical and intuitionistic logic. We then study the
reduction of classical and, derivatively, intuitionistic provability to uniform
provability via the addition to the assumption set of the negation of the
formula to be proved. Our focus here is on understanding the situations in
which this reduction is achieved. However, our discussions indicate the
structure of a proof procedure based on the reduction, a matter also considered
explicitly elsewhere.Comment: 31 page
An Investigation of cultural complexity via memetics: Methodological rationale and its operationalisation
After introducing the background and motivation for my work a portion of my PhD research is presented which considers issues related to the nature of my literature review and the subsequent decisions I have made in respect of an appropriate methodology for empirical work. Literature related to a neo-Darwinian view of human culture is discussed and a number of difficulties related to an absence of consensus amongst theorists are highlighted. The neo-Darwinian perspective demands a replicator in culture which is analogous to the gene in biology and the candidate for that replicator has become know as the meme. The abduction of a narrative orientated methodology for searching for such a replicator is explained and its application demonstrated through an example of coded data. The analysis is based on a structural narrative approach and in particular on the notion of narrative programmes which interact and perhaps compete in social environments. Following concluding remarks the next steps of my PhD work are described.
KEY WORDS: Meme, Memetics, Narrative, Complexit
An Overview of Schema Theory
The purpose of this paper is to give an introduction to the field of Schema
Theory written by a mathematician and for mathematicians. In particular, we
endeavor to to highlight areas of the field which might be of interest to a
mathematician, to point out some related open problems, and to suggest some
large-scale projects. Schema theory seeks to give a theoretical justification
for the efficacy of the field of genetic algorithms, so readers who have
studied genetic algorithms stand to gain the most from this paper. However,
nothing beyond basic probability theory is assumed of the reader, and for this
reason we write in a fairly informal style.
Because the mathematics behind the theorems in schema theory is relatively
elementary, we focus more on the motivation and philosophy. Many of these
results have been proven elsewhere, so this paper is designed to serve a
primarily expository role. We attempt to cast known results in a new light,
which makes the suggested future directions natural. This involves devoting a
substantial amount of time to the history of the field.
We hope that this exposition will entice some mathematicians to do research
in this area, that it will serve as a road map for researchers new to the
field, and that it will help explain how schema theory developed. Furthermore,
we hope that the results collected in this document will serve as a useful
reference. Finally, as far as the author knows, the questions raised in the
final section are new.Comment: 27 pages. Originally written in 2009 and hosted on my website, I've
decided to put it on the arXiv as a more permanent home. The paper is
primarily expository, so I don't really know where to submit it, but perhaps
one day I will find an appropriate journa
Preprints of Proceedings of GWAI-92
This is a preprint of the proceedings of the German Workshop on Artificial Intelligence (GWAI) 1992. The final version will appear in the Lecture Notes in Artificial Intelligence
Metaphysics Renewed: Kant’s Schematized Categories and the Possibility of Metaphysics
This article considers the significance of Kant’s schematized categories in the Critique of Pure Reason for contemporary metaphysics. I present Kant’s understanding of the schematism and how it functions within his critique of the limits of pure reason. Then I argue that, although the true role of the schemata is a relatively late development in Kant’s thought, it is nevertheless a core notion, and the central task of the first Critique can be sufficiently articulated in the language of the schematism. A surprising result of Kant’s doctrine of the schematism is that a limited form of metaphysics is possible even within the parameters set out in the first Critique. To show this, I offer contrasting examples of legitimate and illegitimate forays into metaphysics in light of the condition of the schematized categories
Constructing Conditional Plans by a Theorem-Prover
The research on conditional planning rejects the assumptions that there is no
uncertainty or incompleteness of knowledge with respect to the state and
changes of the system the plans operate on. Without these assumptions the
sequences of operations that achieve the goals depend on the initial state and
the outcomes of nondeterministic changes in the system. This setting raises the
questions of how to represent the plans and how to perform plan search. The
answers are quite different from those in the simpler classical framework. In
this paper, we approach conditional planning from a new viewpoint that is
motivated by the use of satisfiability algorithms in classical planning.
Translating conditional planning to formulae in the propositional logic is not
feasible because of inherent computational limitations. Instead, we translate
conditional planning to quantified Boolean formulae. We discuss three
formalizations of conditional planning as quantified Boolean formulae, and
present experimental results obtained with a theorem-prover
Abstract Canonical Inference
An abstract framework of canonical inference is used to explore how different
proof orderings induce different variants of saturation and completeness.
Notions like completion, paramodulation, saturation, redundancy elimination,
and rewrite-system reduction are connected to proof orderings. Fairness of
deductive mechanisms is defined in terms of proof orderings, distinguishing
between (ordinary) "fairness," which yields completeness, and "uniform
fairness," which yields saturation.Comment: 28 pages, no figures, to appear in ACM Trans. on Computational Logi
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