16 found
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  1.  21
    The Expressive Power of Second-Order Propositional Modal Logic.Michael Kaminski & Michael Tiomkin - 1996 - Notre Dame Journal of Formal Logic 37 (1):35-43.
    It is shown that the expressive power of second-order propositional modal logic whose modalities are S4.2 or weaker is the same as that of second-order predicate logic.
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  2.  25
    Relational Semantics of the Lambek Calculus Extended with Classical Propositional Logic.Michael Kaminski & Nissim Francez - 2014 - Studia Logica 102 (3):479-497.
    We show that the relational semantics of the Lambek calculus, both nonassociative and associative, is also sound and complete for its extension with classical propositional logic. Then, using filtrations, we obtain the finite model property for the nonassociative Lambek calculus extended with classical propositional logic.
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  3.  40
    Commutation-Augmented Pregroup Grammars and Mildly Context-Sensitive Languages.Nissim Francez & Michael Kaminski - 2007 - Studia Logica 87 (2-3):295-321.
    The paper presents a generalization of pregroup, by which a freely-generated pregroup is augmented with a finite set of commuting inequations, allowing limited commutativity and cancelability. It is shown that grammars based on the commutation-augmented pregroups generate mildly context-sensitive languages. A version of Lambek’s switching lemma is established for these pregroups. Polynomial parsability and semilinearity are shown for languages generated by these grammars.
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  4.  43
    Notions of Sameness by Default and Their Application to Anaphora, Vagueness, and Uncertain Reasoning.Ariel Cohen, Michael Kaminski & Johann A. Makowsky - 2008 - Journal of Logic, Language and Information 17 (3):285-306.
    We motivate and formalize the idea of sameness by default: two objects are considered the same if they cannot be proved to be different. This idea turns out to be useful for a number of widely different applications, including natural language processing, reasoning with incomplete information, and even philosophical paradoxes. We consider two formalizations of this notion, both of which are based on Reiter’s Default Logic. The first formalization is a new relation of indistinguishability that is introduced by default. We (...)
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  5.  19
    Nonstandard Connectives of Intuitionistic Propositional Logic.Michael Kaminski - 1988 - Notre Dame Journal of Formal Logic 29 (3):309-331.
  6.  27
    The Lambek Calculus Extended with Intuitionistic Propositional Logic.Michael Kaminski & Nissim Francez - 2016 - Studia Logica 104 (5):1051-1082.
    We present sound and complete semantics and a sequent calculus for the Lambek calculus extended with intuitionistic propositional logic.
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  7. A Comparative Study of Open Default Theories.Michael Kaminski - 1995 - Artificial Intelligence 77 (2):285-319.
  8.  16
    Calculi for Many-Valued Logics.Michael Kaminski & Nissim Francez - 2021 - Logica Universalis 15 (2):193-226.
    We present a number of equivalent calculi for many-valued logics and prove soundness and strong completeness theorems. The calculi are obtained from the truth tables of the logic under consideration in a straightforward manner and there is a natural duality among these calculi. We also prove the cut elimination theorems for the sequent-like systems.
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  9.  6
    Extending the Lambek Calculus with Classical Negation.Michael Kaminski - 2022 - Studia Logica 110 (2):295-317.
    We present an axiomatization of the non-associative Lambek calculus extended with classical negation for which the frame semantics with the classical interpretation of negation is sound and complete.
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  10.  45
    Extending Free Pregroups with Lower Bounds.Tamar Aizikowitz, Nissim Francez, Daniel Genkin & Michael Kaminski - 2010 - Studia Logica 95 (3):417-441.
    In this paper, we propose an extension of free pregroups with lower bounds on sets of pregroup elements. Pregroup grammars based on such pregroups provide a kind of an algebraic counterpart to universal quantification over type-variables. In particular, we show how our pregroup extensions can be used for pregroup grammars expressing natural-language coordination and extraction.
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  11.  15
    Structural Rules for Multi-Valued Logics.Nissim Francez & Michael Kaminski - 2019 - Logica Universalis 13 (1):65-75.
    We study structural rules in the context of multi-valued logics with finitely-many truth-values. We first extend Gentzen’s traditional structural rules to a multi-valued logic context; in addition, we propos some novel structural rules, fitting only multi-valued logics. Then, we propose a novel definition, namely, structural rules completeness of a collection of structural rules, requiring derivability of the restriction of consequence to atomic formulas by structural rules only. The restriction to atomic formulas relieves the need to concern logical rules in the (...)
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  12.  12
    A Proof-Theoretic Semantics for Exclusion.Nissim Francez & Michael Kaminski - 2017 - Logica Universalis 11 (4):489-505.
    The paper provides a proof-theory for a negative presentation of classical logic based on a single primitive of exclusion, generalizing the known presentation via the binary ‘nand. The completeness is established via deductive equivalence to Gentzens NK/LK systems.
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  13.  8
    De Morgan Interpretation of the Lambek–Grishin Calculus.Michael Kaminski & Nissim Francez - 2020 - Review of Symbolic Logic 13 (4):845-856.
    We present an embedding of the Lambek–Grishin calculus into an extension of the nonassociative Lambek calculus with negation. The embedding is based on the De Morgan interpretation of the dual Grishin connectives.
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  14.  13
    The Modal Logic of Cluster-Decomposable Kripke Interpretations.Michael Tiomkin & Michael Kaminski - 2007 - Notre Dame Journal of Formal Logic 48 (4):511-520.
    We deal with the modal logic of cluster-decomposable Kripke interpretations, present an axiomatization, and prove some additional results regarding this logic.
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  15. A Note on the Stable Model Semantics for Logic Programs.Michael Kaminski - 1997 - Artificial Intelligence 96 (2):467-479.
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  16.  25
    The Elimination of de Re Formulas.Michael Kaminski - 1997 - Journal of Philosophical Logic 26 (4):411-422.
    It is shown that de re formulas are eliminable in the modal logic S5 extended with the axiom scheme □∃xφ ⊃ ∃x□φ.
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