5 research outputs found
Goal driven theorem proving using conceptual graphs and Peirce logic
The thesis describes a rational reconstruction of Sowa's theory of Conceptual
Graphs. The reconstruction produces a theory with a firmer logical foundation than was
previously the case and which is suitable for computation whilst retaining the
expressiveness of the original theory. Also, several areas of incompleteness are
addressed. These mainly concern the scope of operations on conceptual graphs of
different types but include extensions for logics of higher orders than first order. An
important innovation is the placing of negation onto a sound representational basis.
A comparison of theorem proving techniques is made from which the principles of
theorem proving in Peirce logic are identified. As a result, a set of derived inference rules,
suitable for a goal driven approach to theorem proving, is developed from Peirce's beta
rules. These derived rules, the first of their kind for Peirce logic and conceptual graphs,
allow the development of a novel theorem proving approach which has some similarities
to a combined semantic tableau and resolution methodology. With this methodology it is
shown that a logically complete yet tractable system is possible. An important result is the
identification of domain independent heuristics which follow directly from the
methodology. In addition to the theorem prover, an efficient system for the detection of
selectional constraint violations is developed.
The proof techniques are used to build a working knowledge base system in Prolog
which can accept arbitrary statements represented by conceptual graphs and test their
semantic and logical consistency against a dynamic knowledge base. The same proof
techniques are used to find solutions to arbitrary queries. Since the system is logically
complete it can maintain the integrity of its knowledge base and answer queries in a fully
automated manner. Thus the system is completely declarative and does not require any
programming whatever by a user with the result that all interaction with a user is
conversational. Finally, the system is compared with other theorem proving systems
which are based upon Conceptual Graphs and conclusions about the effectiveness of the
methodology are drawn
Plasticity and Creativity in the Logic Notebook
Peirceâs architectonics, far from rigid, is bended by many plastic transformations, deriving from the cenopythagorean categories, the pragmaticist (modal) maxim, the logic of abduction, the synechistic hypotheses and the triadic classification of sciences, among many other tools capable of molding knowledge. Plasticity, in turn, points to interlacements between mathematics and art, and shapes some associated conceptual forces in the boundary of the disciplines: variation, modulation and invariance; transformability, continuity and discreteness; creative emergence. In this article we focus on this third aspect, through bounded, well defined case studies in the Logic Notebook. The first section describes the manuscript and its interest for a study of creativity, leading to a short speculation on âcreative reasonâ and âplastic imaginationâ in Peirce. The second section studies five precise cases of creative emergence in the Logic Notebook: differential relatives, existential graphs, sequence diagrams, triadic logic, translatability. Some major surprises occur in those detailed studies
Graph Theory and Universal Grammar
Tese arquivada ao abrigo da Portaria nÂș 227/2017 de 25 de Julho-Registo de Grau EstrangeiroIn the last few years, Noam Chomsky (1994; 1995; 2000; 2001) has gone quite far in
the direction of simplifying syntax, including eliminating X-bar theory and the levels
of D-structure and S-structure entirely, as well as reducing movement rules to a
combination of the more primitive operations of Copy and Merge. What remain in
the Minimalist Program are the operations Merge and Agree and the levels of LF
(Logical Form) and PF (Phonological form).
My doctoral thesis attempts to offer an economical theory of syntactic structure
from a graph-theoretic point of view (cf. Diestel, 2005), with special emphases on the
elimination of category and projection labels and the Inclusiveness Condition
(Chomsky 1994). The major influences for the development of such a theory have
been Chris Collinsâ (2002) seminal paper âEliminating labelsâ, John Bowers (2001)
unpublished manuscript âSyntactic Relationsâ and the Cartographic Paradigm (see
Belletti, Cinque and Rizziâs volumes on OUP for a starting point regarding this
paradigm).
A syntactic structure will be regarded here as a graph consisting of the set of
lexical items, the set of relations among them and nothing more
CIMODE 2016: 3Âș Congresso Internacional de Moda e Design: proceedings
O CIMODE 2016 Ă© o terceiro Congresso Internacional de Moda e Design, a decorrer de 9 a 12 de maio de 2016 na cidade de Buenos Aires, subordinado ao tema : EM--âTRAMAS. A presente edição Ă© organizada pela Faculdade de Arquitetura, Desenho e Urbanismo da Universidade de Buenos Aires, em conjunto com o Departamento de Engenharia TĂȘxtil da Universidade do Minho e com a ABEPEM â Associação Brasileira de Estudos e Pesquisa em Moda.info:eu-repo/semantics/publishedVersio