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  1. Analogues of Bull’s Theorem for Hybrid Logic.Willem Conradie & Claudette Robinson - 2019 - Logic Journal of the IGPL 27 (3):281-313.
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  • Axiomatizing Hybrid Logic Using Modal Logic.Ian Hodkinson & Louis Paternault - 2010 - Journal of Applied Logic 8 (4):386-396.
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  • Justification Logics and Hybrid Logics.Melvin Fitting - 2010 - Journal of Applied Logic 8 (4):356-370.
    Hybrid logics internalize their own semantics. Members of the newer family of justification logics internalize their own proof methodology. It is an appealing goal to combine these two ideas into a single system, and in this paper we make a start. We present a hybrid/justification version of the modal logic T. We give a semantics, a proof theory, and prove a completeness theorem. In addition, we prove a Realization Theorem, something that plays a central role for justification logics generally. Since (...)
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  • Completeness in Hybrid Type Theory.Carlos Areces, Patrick Blackburn, Antonia Huertas & María Manzano - 2013 - Journal of Philosophical Logic (2-3):1-30.
    We show that basic hybridization (adding nominals and @ operators) makes it possible to give straightforward Henkin-style completeness proofs even when the modal logic being hybridized is higher-order. The key ideas are to add nominals as expressions of type t, and to extend to arbitrary types the way we interpret $@_i$ in propositional and first-order hybrid logic. This means: interpret $@_i\alpha _a$ , where $\alpha _a$ is an expression of any type $a$ , as an expression of type $a$ that (...)
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  • Axioms for Classical, Intuitionistic, and Paraconsistent Hybrid Logic.Torben Braüner - 2006 - Journal of Logic, Language and Information 15 (3):179-194.
    In this paper we give axiom systems for classical and intuitionistic hybrid logic. Our axiom systems can be extended with additional rules corresponding to conditions on the accessibility relation expressed by so-called geometric theories. In the classical case other axiomatisations than ours can be found in the literature but in the intuitionistic case no axiomatisations have been published. We consider plain intuitionistic hybrid logic as well as a hybridized version of the constructive and paraconsistent logic N4.
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  • A Hilbert-Style Axiomatisation for Equational Hybrid Logic.Luís S. Barbosa, Manuel A. Martins & Marta Carreteiro - 2014 - Journal of Logic, Language and Information 23 (1):31-52.
    This paper introduces an axiomatisation for equational hybrid logic based on previous axiomatizations and natural deduction systems for propositional and first-order hybrid logic. Its soundness and completeness is discussed. This work is part of a broader research project on the development a general proof calculus for hybrid logics.
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  • A Logic for Diffusion in Social Networks.Zoé Christoff & Jens Ulrik Hansen - 2015 - Journal of Applied Logic 13 (1):48-77.
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  • Hybrid Counterfactual Logics.Katsuhiko Sano - 2009 - Journal of Logic, Language and Information 18 (4):515-539.
    The purpose of this paper is to argue that the hybrid formalism fits naturally in the context of David Lewis’s counterfactual logic and that its introduction into this framework is desirable. This hybridization enables us to regard the inference “The pig is Mary; Mary is pregnant; therefore the pig is pregnant” as a process of updating local information (which depends on the given situation) by using global information (independent of the situation). Our hybridization also has the following technical advantages: (i) (...)
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  • Axiomatizing Hybrid Products.Katsuhiko Sano - 2010 - Journal of Applied Logic 8 (4):459-474.
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  • Completeness in Equational Hybrid Propositional Type Theory.Maria Manzano, Manuel Martins & Antonia Huertas - forthcoming - Studia Logica:1-40.
    Equational hybrid propositional type theory ) is a combination of propositional type theory, equational logic and hybrid modal logic. The structures used to interpret the language contain a hierarchy of propositional types, an algebra and a Kripke frame. The main result in this paper is the proof of completeness of a calculus specifically defined for this logic. The completeness proof is based on the three proofs Henkin published last century: Completeness in type theory, The completeness of the first-order functional calculus (...)
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  • Completeness in Hybrid Type Theory.Carlos Areces, Patrick Blackburn, Antonia Huertas & María Manzano - 2014 - Journal of Philosophical Logic 43 (2-3):209-238.
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