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George Tourlakis [12]George J. Tourlakis [3]
  1.  56
    On the Proof-Theory of Two Formalisations of Modal First-Order Logic.Yehuda Schwartz & George Tourlakis - 2010 - Studia Logica 96 (3):349-373.
    We introduce a Gentzen-style modal predicate logic and prove the cut-elimination theorem for it. This sequent calculus of cut-free proofs is chosen as a proxy to develop the proof-theory of the logics introduced in [14, 15, 4]. We present syntactic proofs for all the metatheoretical results that were proved model-theoretically in loc. cit. and moreover prove that the form of weak reflection proved in these papers is as strong as possible.
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  2.  12
    A Short and Readable Proof of Cut Elimination for Two First-Order Modal Logics.Feng Gao & George Tourlakis - 2015 - Bulletin of the Section of Logic 44 (3/4).
  3.  20
    On the Proof-Theory of a First-Order Extension of GL.Yehuda Schwartz & George Tourlakis - 2014 - Logic and Logical Philosophy 23 (3).
    We introduce a first order extension of GL, called ML 3 , and develop its proof theory via a proxy cut-free sequent calculus GLTS. We prove the highly nontrivial result that cut is a derived rule in GLTS, a result that is unavailable in other known first-order extensions of GL. This leads to proofs of weak reflection and the related conservation result for ML 3 , as well as proofs for Craig’s interpolation theorem for GLTS. Turning to semantics we prove (...)
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  4.  13
    Theory of Computation.George J. Tourlakis - 2012 - Wiley.
    In addition, this book contains tools that, in principle, can search a set of algorithms to see whether a problem is solvable, or more specifically, if it can be solved by an algorithm whose computations are efficient.
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  5.  19
    5. The Main Conservation Requirement.George Tourlakis & Francisco Kibedi - 2004 - Bulletin of the Section of Logic 33 (1):1-10.
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  6.  7
    A New Arithmetically Incomplete First-Order Extension of Gl All Theorems of Which Have Cut Free Proofs.George Tourlakis - 2016 - Bulletin of the Section of Logic 45 (1).
    Reference [12] introduced a novel formula to formula translation tool that enables syntactic metatheoretical investigations of first-order modallogics, bypassing a need to convert them first into Gentzen style logics in order torely on cut elimination and the subformula property. In fact, the formulator tool,as was already demonstrated in loc. cit., is applicable even to the metatheoreticalstudy of logics such as QGL, where cut elimination is unavailable. This paper applies the formulator approach to show the independence of the axiom schema ☐A (...)
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  7.  14
    A New Foundation of a Complete Boolean Equational Logic.George Tourlakis - 2009 - Bulletin of the Section of Logic 38 (1/2):13-28.
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  8.  15
    Pure Iteration and Substitution as the Basis of Computability.Yehuda Schwartz & George Tourlakis - 2011 - Bulletin of the Section of Logic 40 (3/4):203-213.
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  9.  24
    Lectures in Logic and Set Theory: Volume 1, Mathematical Logic.George J. Tourlakis - 2003 - Cambridge University Press.
    This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a user-friendly conversational lecture style that makes them equally effective for self-study or class use. Volume II, on formal (ZFC) set theory, incorporates a self-contained 'chapter 0' on proof techniques so (...)
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  10.  13
    Recursion in Partial Type‐1 Objects With Well‐Behaved Oracles.George Tourlakis - 1996 - Mathematical Logic Quarterly 42 (1):449-460.
    We refine the definition of II-computability of [12] so that oracles have a “consistent”, but natural, behaviour. We prove a Kleene Normal Form Theorem and closure of semi-recursive relations under ∃1. We also show that in this more inclusive computation theory Post's theorem in the arithmetical hierarchy still holds.
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