Kripke Semantics for Martin-L\"of's Extensional Type Theory by Steve Awodey, Florian Rabe

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Dualising Intuitionistic Negation by Graham Priest

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Unification and Finite Model Property for Linear Step-Like Temporal Multi-Agent Logic with the Universal Modality by Stepan I. Bashmakov, Tatyana Yu. Zvereva

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Postmodern Fuzzy System Theory: A Deconstruction Approach Based on Kabbalah by Gabriel Burstein, Constantin Virgil Negoita, Menachem Kranz

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A Comparison of Implications in Orthomodular Quantum Logic—Morphological Analysis of Quantum Logic by Mitsuhiko Fujio

“…In particular, morphology for set lattices is applied to analyze logics through Kripke semantics (Bloch, 2002; Fujio and Bloch, 2004; Fujio, 2006). …”
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Towards a Proof Theory of G\"odel Modal Logics by George Metcalfe, Nicola Olivetti

“…Analytic proof calculi are introduced for box and diamond fragments of basic modal fuzzy logics that combine the Kripke semantics of modal logic K with the many-valued semantics of G\"odel logic. …”
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Convolution Algebras: Relational Convolution, Generalised Modalities and Incidence Algebras by Brijesh Dongol, Ian J. Hayes, Georg Struth

“…Convolution is a ubiquitous operation in mathematics and computing. The Kripke semantics for substructural and interval logics motivates its study for quantale-valued functions relative to ternary relations. …”
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Dualising Intuitionictic Negation by Graham Priest

“…A logic is defined by taking the Kripke semantics for intuitionistic logic, and dualising the truth conditions for negation. …”
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Forensic Dynamic Lukasiewicz Logic by Antonio Di Nola, Revaz Grigolia

“…A forensic dynamic $n$-valued Lukasiewicz logic $FDL_n$ is introduced on the base of $n$-valued Lukasiewicz logic $L_n$ and corresponding to it forensic dynamic $MV_n$-algebra ($FDL_n$-algebra)‎, ‎$1 < n < \omega$‎, ‎which are algebraic counterparts of the logic‎, ‎that in turn represent two-sorted algebras $(\mathcal{M}‎, ‎\mathcal{R}‎, ‎\Diamond)$ that combine the varieties of $MV_n$-algebras $\mathcal{M} = (M‎, ‎\oplus‎, ‎\odot‎, ‎\sim‎, ‎0,1)$ and regular algebras $\mathcal{R} = (R,\cup‎, ‎;‎, ‎^\ast)$ into a single finitely axiomatized variety resemblig $R$-module with‎ ‎"scalar"‎ ‎multiplication $\Diamond$‎. ‎Kripke semantics is developed for forensic dynamic Lukasiewicz logic $FDL_n$ with application to Digital Forensics‎.…”
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Intuitionistic Layered Graph Logic: Semantics and Proof Theory by Simon Docherty, David Pym

“…We give soundness and completeness theorems for a labelled tableaux system with respect to a Kripke semantics on graphs. We then give an equivalent relational semantics, itself proven equivalent to an algebraic semantics via a representation theorem. …”
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Varieties of unary-determined distributive $\ell$-magmas and bunched implication algebras by Natanael Alpay, Peter Jipsen, Melissa Sugimoto

“…We also provide Kripke semantics for the algebras under consideration, which leads to more efficient algorithms for constructing finite models. …”
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A Logical Foundation for Environment Classifiers by Takeshi Tsukada, Atsushi Igarashi

“…Finally, we show that the proof system augmented with a classical axiom is sound and complete with respect to a Kripke semantics of the logic.…”
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Reasoning About the Transfer of Control by Hoek, W, Walther, D, Wooldridge, M

“…We give two alternative semantics for the logic: a direct semantics, in which we capture the distributions of Boolean variables to agents; and a more conventional Kripke semantics. We prove that these semantics are equivalent, and then present an axiomatization for the logic. …”