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  1.  5
    Modal Definability: Two Commuting Equivalence Relations.Yana Rumenova & Tinko Tinchev - 2022 - Logica Universalis 16 (1):177-194.
    We prove that modal definability with respect to the class of all structures with two commuting equivalence relations is an undecidable problem. The construction used in the proof shows that the same is true for the subclass of all finite structures. For that reason we prove that the first-order theories of these classes are undecidable and reduce the latter problem to the former.
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  2.  2
    Remarks About the Unification Types of Some Locally Tabular Normal Modal Logics.Philippe Balbiani, ÇiĞdem Gencer, Maryam Rostamigiv & Tinko Tinchev - forthcoming - Logic Journal of the IGPL.
    It is already known that unifiable formulas in normal modal logic $\textbf {K}+\square ^{2}\bot $ are either finitary or unitary and unifiable formulas in normal modal logic $\textbf {Alt}_{1}+\square ^{2}\bot $ are unitary. In this paper, we prove that for all $d{\geq }3$, unifiable formulas in normal modal logic $\textbf {K}+\square ^{d}\bot $ are either finitary or unitary and unifiable formulas in normal modal logic $\textbf {Alt}_{1}+\square ^{d}\bot $ are unitary.
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  3. Definability and Computability for PRSPDL.Philippe Balbiani & Tinko Tinchev - 2014 - In Rajeev Goré, Barteld Kooi & Agi Kurucz (eds.), Advances in Modal Logic, Volume 10. CSLI Publications. pp. 16-33.
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  4.  1
    Unification in Modal Logic Alt1.Philippe Balbiani & Tinko Tinchev - 2016 - In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11. CSLI Publications. pp. 117-134.
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  5.  14
    Dynamic Logics of the Region-Based Theory of Discrete Spaces.Philippe Balbiani, Tinko Tinchev & Dimiter Vakarelov - 2007 - Journal of Applied Non-Classical Logics 17 (1):39-61.
    The aim of this paper is to give new kinds of modal logics suitable for reasoning about regions in discrete spaces. We call them dynamic logics of the region-based theory of discrete spaces. These modal logics are linguistic restrictions of propositional dynamic logic with the global diamond E. Their formulas are equivalent to Boolean combinations of modal formulas like E where A and B are Boolean terms and α is a relational term. Examining what we can say about dynamic models (...)
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  6.  8
    Line-Based Affine Reasoning in Euclidean Plane.Philippe Balbiani & Tinko Tinchev - 2007 - Journal of Applied Logic 5 (3):421-434.
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  7.  18
    Mixed Algebras and Their Logics.Ivo Düntsch, Ewa Orłowska & Tinko Tinchev - 2017 - Journal of Applied Non-Classical Logics 27 (3-4):304-320.
    We investigate complex algebras of the form arising from a frame where, and exhibit their abstract algebraic and logical counterparts.
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  8.  14
    Second-Order Logic on Equivalence Relations.Georgi Georgiev & Tinko Tinchev - 2008 - Journal of Applied Non-Classical Logics 18 (2-3):229-246.
    In this paper we investigate several extensions of the first order-language with finitely many binary relations. The most interesting of the studied extensions appears to be the monadic second-order one. We show that the extended languages have the same expressive power as the first-order language over the class of all relational structures of equivalence relations in local agreement by providing appropriate translation of formulae. The decidability of the considered extensions over the above mentioned class of structures is also shown.
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  9.  4
    Logics of Space with Connectedness Predicates: Complete Axiomatizations.Tinko Tinchev & Dimiter Vakarelov - 2010 - In Lev Beklemishev, Valentin Goranko & Valentin Shehtman (eds.), Advances in Modal Logic, Volume 8. CSLI Publications. pp. 434-453.
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  10.  10
    Foreword.Philippe Balbiani & Tinko Tinchev - 2008 - Journal of Applied Non-Classical Logics 18 (2-3):135-135.