No description available.

Bertrand Russell's works on logic, despite his reputation as a founder of mathematical logic, appear unnecessarily metaphysical and even naïve to contemporary logicians and philosophers. He offered several accounts of logic whilst pursuing the goal of logicism, the view of mathematics as reducible to logic. In their attempts to explain why those accounts look naïve nowadays, many commentators have sought one or another simple philosophical doctrine which can characterise his conception of logic. Instead of thus assuming a coherent theme underlying his works on logic, I propose to understand them as a shift from a conception of logic towards another. By looking into books, papers and manuscripts which he wrote during the period from 1898 to 1918, I argue that he inherited an antique, metaphysical conception of logic from his idealist predecessors and, through his attempts to replace some idealistic features of the conception with his realist alternatives, he became more sympathetic to—though never fully convinced of—a linguistic conception of logic, which was proposed by some of his contemporary logicians and has been widely accepted since then.

by Hwang Hoi Yee Cothan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 68-70). / Abstract --- p.ii / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Objectives of the Thesis --- p.1 / Chapter 1.2 --- Overview of the Thesis --- p.7 / Chapter 2 --- Background and Related Work --- p.8 / Chapter 2.1 --- Deductive Databases --- p.8 / Chapter 2.2 --- Disjunctive Deductive Databases --- p.10 / Chapter 2.3 --- Model tree for disjunctive deductive databases --- p.11 / Chapter 3 --- Preliminary --- p.13 / Chapter 3.1 --- Disjunctive Logic Program --- p.13 / Chapter 3.2 --- Data-disjunctive Logic Program --- p.14 / Chapter 4 --- Semantics of Data-disjunctive Logic Program --- p.17 / Chapter 4.1 --- Model-theoretic semantics --- p.17 / Chapter 4.2 --- Fixpoint semantics --- p.20 / Chapter 4.2.1 --- Fixpoint operators corresponding to the MMSpDD --- p.22 / Chapter 4.2.2 --- "Fixpoint operator corresponding to the contingency model, CMP" --- p.25 / Chapter 4.3 --- Equivalence between the model-theoretic and fixpoint semantics --- p.26 / Chapter 4.4 --- Operational Semantics --- p.30 / Chapter 4.5 --- Correspondence with the I-table --- p.31 / Chapter 5 --- Disjunctive Deductive Databases --- p.33 / Chapter 5.1 --- Disjunctions in deductive databases --- p.33 / Chapter 5.2 --- Relation between predicates --- p.35 / Chapter 5.3 --- Transformation of Disjunctive Deductive Data-bases --- p.38 / Chapter 5.4 --- Query answering for Disjunctive Deductive Data-bases --- p.40 / Chapter 6 --- Magic for Data-disjunctive Deductive Database --- p.44 / Chapter 6.1 --- Magic for Relevant Answer Set --- p.44 / Chapter 6.1.1 --- Rule rewriting algorithm --- p.46 / Chapter 6.1.2 --- Bottom-up evaluation --- p.49 / Chapter 6.1.3 --- Examples --- p.49 / Chapter 6.1.4 --- Discussion on the rewriting algorithm --- p.52 / Chapter 6.2 --- Alternative algorithm for Traditional Answer Set --- p.54 / Chapter 6.2.1 --- Rule rewriting algorithm --- p.54 / Chapter 6.2.2 --- Examples --- p.55 / Chapter 6.3 --- Contingency answer set --- p.56 / Chapter 7 --- Experiments and Comparison --- p.57 / Chapter 7.1 --- Experimental Results --- p.57 / Chapter 7.1.1 --- Results for the Traditional answer set --- p.58 / Chapter 7.1.2 --- Results for the Relevant answer set --- p.61 / Chapter 7.2 --- Comparison with the evaluation method for Model tree --- p.63 / Chapter 8 --- Conclusions and Future Work --- p.66 / Bibliography --- p.68

Tese de mestrado integrado. Engenharia Informática e Computação. Faculdade de Engenharia. Universidade do Porto. 2010

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The focus of this thesis is to introduce the concept of Kähler-Poisson algebras as analogues of algebras of smooth functions on Kähler manifolds. We first give here a review of the geometry of Kähler manifolds and Lie-Rinehart algebras. After that we give the definition and basic properties of Kähler-Poisson algebras. It is then shown that the Kähler type condition has consequences that allow for an identification of geometric objects in the algebra which share several properties with their classical counterparts. Furthermore, we introduce a concept of morphism between Kähler-Poisson algebras and show its consequences. Detailed examples are provided in order to illustrate the novel concepts. / <p>The series name is corrected in the electronic version of the cover.</p>

In this thesis we are concerned with developing formal and representational mechanisms for reasoning with inconsistent information. Strictly speaking there are two conceptually distinct senses in which we are interested in reasoning with inconsistent information. In one sense, we are interested in using logical deduction to draw inferences in a symbolic system. More specifically, we are interested in mechanisms that can continue to perform deduction in a reasonable manner despite the threat of inconsistencies as a direct result of errors or misrepresentations. So in this sense we are interested in inconsistency-tolerant or paraconsistent deduction. ¶ However, not every case of inconsistent description is a case of misrepresentation. In many practical situations, logically inconsistent descriptions may be deployed as representations for problems that are inherently conflicting. The issue of error or misrepresentation is irrelevant in these cases. Rather the main concern in these cases is to provide meaningful analyses of the underlying structure and properties of our logical representation which in turn informs us about the salient features of the problem under consideration. So in this second sense, we are interested in deploying logic as a representation to model situations involving conflict. ¶ In this thesis we adopt a novel framework to unify both logic-as-deduction and logic-as-representation approaches to reasoning with inconsistent information. From a preservational view point, we take deduction as a process by which metalogical properties are preserved from premises to conclusions. Thus methodologically we may begin by identifying inconsistency-tolerant deduction mechanisms and then investigate what additional properties of inconsistent premises are preserved by these mechanisms; or alternatively we may begin by identifying properties of inconsistent logical descriptions and investigate which deductive mechanisms can preserve these properties. We view these as two aspects of the same investigation. A key assumption in this work is that adequate analyses of inconsistencies require provisions to quantitatively measure and compare inconsistent logical representations. While paraconsistent logics have enjoyed considerable success in recent years, proper quantitative analysis of inconsistencies seems to have lapsed behind to some extent. In this thesis we’ll explore different ways in which we can compare and measure inconsistencies. We hope to show that both inference and analysis can fruitfully be brought to bear on the issue of inconsistency handling under the same methodological scheme.

This thesis examines a novel induction-based framework for logic programming. Limiting programs are logic programs distinguished by two features, in general they contain an infinite data stream over which induction will be performed, and in general it is not possible for a system to know when a solution for any program is correct. These facts are characteristic of some problems involving induction in artificial intelligence, and several problems in knowledge representation and logic programming have exactly these properties. This thesis presents a specification language for problems with an inductive nature, limiting programs, and a resolution based system, limiting resolution, for solving these problems. This framework has properties which guarantee that the system will converge upon a particular answer in the limit. Solutions to problems which have such an inductive property by nature can be implemented using the language, and solved with the solver. For instance, many classification problems are inductive by nature. Some generalized planning problems also have the inductive property. For a class of generalized planning problems, we show that identifying a collection of domains where a plan reaches a goal is equivalent to producing a plan. This thesis gives examples of both. Limiting resolution works by a generate-and-test strategy, creating a potential solution and iteratively looking for a contradiction with the growing stream of data provided. Limiting resolution can be implemented by modifying conventional PROLOG technology. The generateand- test strategy has some inherent inefficiencies. Two improvements have arisen from this work; the first is a tabling strategy which records previously failed attempts to produce a solution and thereby avoids redundant test steps. The second is based on the heuristic observation that for some problems the size of the test step is proportional to the closeness of the generated potential-solution to the real solution, in a suitable metric. The observation can be used to improve the performance of limiting resolution. Thus this thesis describes, from theoretical foundations to implementation, a coherent methodology for incorporating induction into existing general A.I. programming techniques, along with examples of how to perform such tasks.

Thesis (M.A.)--Memorial University of Newfoundland, 2005. / Bibliography: leaves 64-70.

Thesis (Ph. D.)--University of Texas at Dallas, 2006. / Includes vita. Includes bibliographical references (leaves 107-114).