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Ildikó Sain [12]I. Sain [5]Ilkidó Sain [1]
  1.  18
    Complexity of Equational Theory of Relational Algebras with Projection Elements.Szabolcs Mikulás, Ildikó Sain & Andras Simon - 1992 - Bulletin of the Section of Logic 21 (3):103-111.
    The class \ of t rue p airing a lgebras is defined to be the class of relation algebras expanded with concrete set theoretical projection functions. The main results of the present paper is that neither the equational theory of \ nor the first order theory of \ are decidable. Moreover, we show that the set of all equations valid in \ is exactly on the \ level. We consider the class \ of the relation algebra reducts of \ ’s, (...)
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  2.  42
    Decidable and Undecidable Logics with a Binary Modality.ágnes Kurucz, István Németi, Ildikó Sain & András Simon - 1995 - Journal of Logic, Language and Information 4 (3):191-206.
    We give an overview of decidability results for modal logics having a binary modality. We put an emphasis on the demonstration of proof-techniques, and hope that this will also help in finding the borderlines between decidable and undecidable fragments of usual first-order logic.
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  3.  17
    Is “Some-Other-Time” Sometimes Better Than “Sometime” for Proving Partial Correctness of Programs?Ildikó Sain - 1988 - Studia Logica 47 (3):279 - 301.
    The main result of this paper belongs to the field of the comparative study of program verification methods as well as to the field called nonstandard logics of programs. We compare the program verifying powers of various well-known temporal logics of programs, one of which is the Intermittent Assertions Method, denoted as Bur. Bur is based on one of the simplest modal logics called S5 or sometime-logic. We will see that the minor change in this background modal logic increases the (...)
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  4.  24
    Structured Nonstandard Dynamic Logic.Ildikó Sain - 1984 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 30 (31):481-497.
  5.  9
    Undecidability of the Equational Theory of Some Classes of Residuated Boolean Algebras with Operators.I. Nemeti, I. Sain & A. Simon - 1995 - Logic Journal of the IGPL 3 (1):93-105.
    We show the undecidability of the equational theories of some classes of BAOs with a non-associative, residuated binary extra-Boolean operator. These results solve problems in Jipsen [9], Pratt [21] and Roorda [22], [23]. This paper complements Andréka-Kurucz-Németi-Sain-Simon [3] where the emphasis is on BAOs with an associative binary operator.
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  6.  4
    Undecidable Varieties of Semilattice—Ordered Semigroups, of Boolean Algebras with Operators, and Logics Extending Lambek Calculus.A. Kurucz, I. Nemeti, I. Sain & A. Simon - 1993 - Logic Journal of the IGPL 1 (1):91-98.
    We prove that the equational theory of a semigroups becomes undecidable if we add a semilattice structure with a ‘touch of symmetric difference’. As a corollary we obtain that the variety of all Boolean algebras with an associative binary operator has a ‘hereditarily’ undecidable equational theory. Our results have implications in logic, e.g. they imply undecidability of modal logics extending the Lambek Calculus and undecidability of Arrow Logics with an associative arrow modality.
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  7.  14
    Complexity of Equational Theory of Relational Algebras with Standard Projection Elements.Szabolcs Mikulás, Ildikó Sain & András Simon - 2015 - Synthese 192 (7):2159-2182.
    The class $$\mathsf{TPA}$$ TPA of t rue p airing a lgebras is defined to be the class of relation algebras expanded with concrete set theoretical projection functions. The main results of the present paper is that neither the equational theory of $$\mathsf{TPA}$$ TPA nor the first order theory of $$\mathsf{TPA}$$ TPA are decidable. Moreover, we show that the set of all equations valid in $$\mathsf{TPA}$$ TPA is exactly on the $$\Pi ^1_1$$ Π 1 1 level. We consider the class $$\mathsf{TPA}^-$$ (...)
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  8.  5
    Structured Nonstandard Dynamic Logic.Ildikó Sain - 1984 - Mathematical Logic Quarterly 30 (31):481-497.
  9.  17
    Computer Science Temporal Logics Need Their Clocks.Ildikó Sain - 1989 - Bulletin of the Section of Logic 18 (4):153-160.
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  10. Total Correctness in Nonstandard Dynamic Logic.Ildiko Sain - 1983 - Bulletin of the Section of Logic 12 (2):64-68.
    In this paper we investigate total correctness in Nonstandard Dynamic Logic . Here we show that despite of the celebrated Kfoury-Park [5] result, termination is a rst order notion if approached properly.
     
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  11.  9
    Peano Arithmetic as Axiomatization of the Time Frame in Logics of Programs and in Dynamic Logics.Balázs Biró & Ildikó Sain - 1993 - Annals of Pure and Applied Logic 63 (3):201-225.
    Biró, B. and I. Sain, Peano arithmetic as axiomatization of the time frame in logics of programs and in dynamic logics, Annals of Pure and Applied Logic 63 201-225. We show that one can prove the partial correctness of more programs using Peano's axioms for the time frames of three-sorted time models than using only Presburger's axioms, that is it is useful to allow multiplication of time points at program verification and in dynamic and temporal logics. We organized the paper (...)
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  12.  6
    Concerning Some Cylindric Algebra Versions of the Downward Löwenheim-Skolem Theorem.Ildikó Sain - 1988 - Notre Dame Journal of Formal Logic 29 (3):332-344.
  13.  3
    An Elementary Proof for Some Semantic Characterizations of Nondeterministic Floyd-Hoare Logic.Ildikó Sain - 1989 - Notre Dame Journal of Formal Logic 30 (4):563-573.
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  14.  1
    Editorial.I. Németi & I. Sain - 2000 - Logic Journal of the IGPL 8 (4):379-381.
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  15. Program Verification Within and Without Logic.Hajnal Andreka, Istvan Nemeti & Ildiko Sain - 1979 - Bulletin of the Section of Logic 8 (3):124-128.
    Theorem 1 states a negative result about the classical semantics j= ! of program schemes. Theorem 2 investigates the reason for this. We conclude that Theorem 2 justies the Henkin-type semantics j= for which the opposite of the present Theorem 1 was proved in [1]{[3] and also in a dierent form in part III of [5]. The strongest positive result on j= is Corollary 6 in [3].
     
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