6 found
Eugenio Omodeo [3]Eugenio G. Omodeo [3]Eugenio Giovanni Omodeo [1]
  1. Decidability of ∀*∀‐Sentences in Membership Theories.Eugenio G. Omodeo, Franco Parlamento & Alberto Policriti - 1996 - Mathematical Logic Quarterly 42 (1):41-58.
    The problem is addressed of establishing the satisfiability of prenex formulas involving a single universal quantifier, in diversified axiomatic set theories. A rather general decision method for solving this problem is illustrated through the treatment of membership theories of increasing strength, ending with a subtheory of Zermelo-Fraenkel which is already complete with respect to the ∀*∀ class of sentences. NP-hardness and NP-completeness results concerning the problems under study are achieved and a technique for restricting the universal quantifier is presented.
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  2.  1
    An Environment for Specifying Properties of Dyadic Relations and Reasoning About Them II: Relational Presentation of Non-Classical Logics.Andrea Formisano, Eugenio G. Omodeo & Ewa Orłowska - 2006 - In Harrie de Swart, Ewa Orlowska, Gunther Smith & Marc Roubens (eds.), Theory and Applications of Relational Structures as Knowledge Instruments Ii. Springer. pp. 89--104.
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  3.  9
    The Axiom of Elementary Sets on the Edge of Peircean Expressibility.Andrea Formisano, Eugenio G. Omodeo & Alberto Policriti - 2005 - Journal of Symbolic Logic 70 (3):953 - 968.
    Being able to state the principles which lie deepest in the foundations of mathematics by sentences in three variables is crucially important for a satisfactory equational rendering of set theories along the lines proposed by Alfred Tarski and Steven Givant in their monograph of 1987. The main achievement of this paper is the proof that the 'kernel' set theory whose postulates are extensionality. (E), and single-element adjunction and removal. (W) and (L), cannot be axiomatized by means of three-variable sentences. This (...)
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    The Bernays-Schönfinkel-Ramsey Class for Set Theory: Semidecidability.Eugenio Omodeo & Alberto Policriti - 2010 - Journal of Symbolic Logic 75 (2):459-480.
    As is well-known, the Bernays-Schönfinkel-Ramsey class of all prenex ∃*∀* -sentences which are valid in classical first-order logic is decidable. This paper paves the way to an analogous result which the authors deem to hold when the only available predicate symbols are ∈ and =, no constants or function symbols are present, and one moves inside a (rather generic) Set Theory whose axioms yield the well-foundedness of membership and the existence of infinite sets. Here semi-decidability of the satisfiability problem for (...)
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    The Bernays—Schönfinkel—Ramsey Class for Set Theory: Decidability.Alberto Policriti & Eugenio Omodeo - 2012 - Journal of Symbolic Logic 77 (3):896-918.
    As proved recently, the satisfaction problem for all prenex formulae in the set-theoretic Bernays-Shönfinkel-Ramsey class is semi-decidable over von Neumann's cumulative hierarchy. Here that semi-decidability result is strengthened into a decidability result for the same collection of formulae.
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    Three Existence Principles in a Modal Calculus Without Descriptions Contained in A. Bressan's ${\Rm MC}^\Nu$.Eugenio Giovanni Omodeo - 1980 - Notre Dame Journal of Formal Logic 21 (4):711-727.