Titlebook: Logic and Its Applications; Third Indian Confere R. Ramanujam,Sundar Sarukkai Conference proceedings 2009 Springer-Verlag Berlin Heidelberg

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Machine Checking Proof Theory: An Application of Logic to Logic,Modern proof-assistants are now mature enough to formalise many aspects of mathematics. I outline some work we have done using the proof-assistant Isabelle to machine-check aspects of proof theory in general, and specifically the proof theory of provability logic GL.

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AGONY

Instantial Relevance in Polyadic Inductive Logic,We show that under the assumptions of Spectrum Exchangeability and Language Invariance the so called ., a principle of instantial relevance previously know for unary (i.e. classical) Carnapian Inductive Logic, also holds in Polyadic Inductive Logic.

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A Unified Framework for Certificate and Compilation for QBF,We propose in this article a unified framework for certificate and compilation for QBF. We provide a search-based algorithm to compute a certificate for the validity of a QBF and a search-based algorithm to compile a valid QBF in our unified framework.

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Towards Decidability of Conjugacy of Pairs and Triples,The equation .?=?. is called the conjugacy equation. Here ., . and . are languages over a finite alphabet. Given two sets . and ., we can ask “Does there exist a . which makes the conjugacy equation true?”. We answer this question partially in the case when one of them is a two element set and the other is a three element set.

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https://doi.org/10.1007/978-3-540-92701-3LA; algorithms; analytic proof theory; artificial intelligence; automata; calculi; combinatorics; complexit

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978-3-540-92700-6Springer-Verlag Berlin Heidelberg 2009

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Logic and Its Applications978-3-540-92701-3Series ISSN 0302-9743 Series E-ISSN 1611-3349

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Extensive Questions,t to Olsson’s own. We conclude arguing that: (.) our solution makes the idea of ‘minimal change’ in questions and agendas clearer; (.) can be extended in ways the original theory was not, and may help better realize the aims this theory was proposed for; (.) unveils some limitations of the initial approach, yet opening a way to overcome them.

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