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    An exploration in fluid logics

    Author
    Taylor, Joshua
    View/Open
    174848_Taylor_rpi_0185E_10553.pdf (1.029Mb)
    Other Contributors
    Bringsjord, Selmer; Goldberg, Mark; Varela, Carlos A.; Cassimatis, Nicholas L. (Nicholas Louis), 1971-;
    Date Issued
    2014-12
    Subject
    Computer science
    Degree
    PhD;
    Terms of Use
    This electronic version is a licensed copy owned by Rensselaer Polytechnic Institute, Troy, NY. Copyright of original work retained by author.;
    Metadata
    Show full item record
    URI
    https://hdl.handle.net/20.500.13015/1323
    Abstract
    We designed and implemented a framework, programming language, and standard library for specifying and programming in categorical denotational proof languages. We encoded a number of logical systems, including several versions of the propositional calculus, and mappings between them, including a mapping based on a translation between axiomatic proofs into natural-deduction proofs, and a mapping based on the deduction theorem. We present examples illustrating how programs in this language achieve heterogeneous reasoning, and conclude with discussion of future work and applications.; Human reasoning is heterogeneous. Whether reasoning formally or informally, human reasoners frequently and effortlessly switch between many problem representations, reapplying results and techniques from one domain in another. Research in artificial intelligence, on the other hand, often produces "mechanical savants" that can solve one problem incredibly well, but are completely inapplicable to any other. In this dissertation, we set out to investigate and implement formal methods and techniques that capture the heterogeneity of formal human reasoning.; We review the ways in which combinations of logical systems have been used in mathematics and artificial intelligence, and the types of results that have been realized though mappings between logics and proof systems. We identify areas of research that are especially promising in automated reasoning and the representation of logical systems: denotational proof languages and category theory. Denotational proof languages are a family of languages that integrate deduction and computation. Category theory is an abstract branch of mathematics that provides a high level of generality and unites, among other things, many different types of logical systems.; Fusing denotational proof languages and category theory, we develop categorical denotational proof languages. These are a variant of denotational proof languages that take proofs, realized as categorical arrows, rather than propositions, as a fundamental building block. We demonstrate that category theory is a suitable formalism for representing logical systems and the mappings between them, and that categorical denotational proof languages are an effective tool for specifying the relationships between logical systems and the transformations between them, and do so in a way that promotes proof reuse.;
    Description
    December 2014; School of Science
    Department
    Dept. of Computer Science;
    Publisher
    Rensselaer Polytechnic Institute, Troy, NY
    Relationships
    Rensselaer Theses and Dissertations Online Collection;
    Access
    Restricted to current Rensselaer faculty, staff and students. Access inquiries may be directed to the Rensselaer Libraries.;
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    • RPI Theses Online (Complete)

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