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Relevant bibliographies by topics / Modal logic

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Academic literature on the topic 'Modal logic'

Author: Grafiati

Published: 4 June 2021

Last updated: 6 July 2024

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Journal articles on the topic "Modal logic"

1

Schumann, Andrew. "Nāgārjunian-Yogācārian Modal Logic versus Aristotelian Modal Logic." Journal of Indian Philosophy 49, no. 3 (May 26, 2021): 467–98. http://dx.doi.org/10.1007/s10781-021-09470-5.

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AbstractThere are two different modal logics: the logic T assuming contingency and the logic K = assuming logical determinism. In the paper, I show that the Aristotelian treatise On Interpretation (Περί ερμηνείας, De Interpretatione) has introduced some modal-logical relationships which correspond to T. In this logic, it is supposed that there are contingent events. The Nāgārjunian treatise Īśvara-kartṛtva-nirākṛtiḥ-viṣṇoḥ-ekakartṛtva-nirākaraṇa has introduced some modal-logical relationships which correspond to K =. In this logic, it is supposed that there is a logical determinism: each event happens necessarily (siddha) or it does not happen necessarily (asiddha). The Nāgārjunian approach was inherited by the Yogācārins who developed, first, the doctrine of causality of all real entities (arthakriyātva) and, second, the doctrine of momentariness of all real entities (kṣaṇikavāda). Both doctrines were a philosophical ground of the Yogācārins for the logical determinism. Hence, Aristotle implicitly used the logic T in his modal reasoning. The Madhyamaka and Yogācāra schools implicitly used the logic K = in their modal reasoning.

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Rybakov, V. V. "Hereditarily structurally complete modal logics." Journal of Symbolic Logic 60, no. 1 (March 1995): 266–88. http://dx.doi.org/10.2307/2275521.

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AbstractWe consider structural completeness in modal logics. The main result is the necessary and sufficient condition for modal logics over K4 to be hereditarily structurally complete: a modal logic λ is hereditarily structurally complete iff λ is not included in any logic from the list of twenty special tabular logics. Hence there are exactly twenty maximal structurally incomplete modal logics above K4 and they are all tabular.

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Kooi, Barteld, and Allard Tamminga. "Three-valued Logics in Modal Logic." Studia Logica 101, no. 5 (August 21, 2012): 1061–72. http://dx.doi.org/10.1007/s11225-012-9420-0.

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BEZHANISHVILI, GURAM, NICK BEZHANISHVILI, and JULIA ILIN. "STABLE MODAL LOGICS." Review of Symbolic Logic 11, no. 3 (September 2018): 436–69. http://dx.doi.org/10.1017/s1755020317000375.

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AbstractStable logics are modal logics characterized by a class of frames closed under relation preserving images. These logics admit all filtrations. Since many basic modal systems such as K4 and S4 are not stable, we introduce the more general concept of an M-stable logic, where M is an arbitrary normal modal logic that admits some filtration. Of course, M can be chosen to be K4 or S4. We give several characterizations of M-stable logics. We prove that there are continuum many S4-stable logics and continuum many K4-stable logics between K4 and S4. We axiomatize K4-stable and S4-stable logics by means of stable formulas and discuss the connection between S4-stable logics and stable superintuitionistic logics. We conclude the article with many examples (and nonexamples) of stable, K4-stable, and S4-stable logics and provide their axiomatization in terms of stable rules and formulas.

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Demey, Lorenz. "Logic-Sensitivity of Aristotelian Diagrams in Non-Normal Modal Logics." Axioms 10, no. 3 (June 22, 2021): 128. http://dx.doi.org/10.3390/axioms10030128.

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Aristotelian diagrams, such as the square of opposition, are well-known in the context of normal modal logics (i.e., systems of modal logic which can be given a relational semantics in terms of Kripke models). This paper studies Aristotelian diagrams for non-normal systems of modal logic (based on neighborhood semantics, a topologically inspired generalization of relational semantics). In particular, we investigate the phenomenon of logic-sensitivity of Aristotelian diagrams. We distinguish between four different types of logic-sensitivity, viz. with respect to (i) Aristotelian families, (ii) logical equivalence of formulas, (iii) contingency of formulas, and (iv) Boolean subfamilies of a given Aristotelian family. We provide concrete examples of Aristotelian diagrams that illustrate these four types of logic-sensitivity in the realm of normal modal logic. Next, we discuss more subtle examples of Aristotelian diagrams, which are not sensitive with respect to normal modal logics, but which nevertheless turn out to be highly logic-sensitive once we turn to non-normal systems of modal logic.

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Venema, Yde, Alexander Chagrov, and Michael Zakharyaschev. "Modal Logic." Philosophical Review 109, no. 2 (April 2000): 286. http://dx.doi.org/10.2307/2693587.

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Kracht, Marcus, Patrick Blackburn, Maarten de Rijke, and Yde Venema. "Modal Logic." Bulletin of Symbolic Logic 8, no. 2 (June 2002): 299. http://dx.doi.org/10.2307/2693968.

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Venema, Y. "MODAL LOGIC." Philosophical Review 109, no. 2 (April 1, 2000): 286–89. http://dx.doi.org/10.1215/00318108-109-2-286.

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Spencer-Smith, Richard. "Modal logic." Artificial Intelligence Review 5, no. 1-2 (1991): 5–34. http://dx.doi.org/10.1007/bf00129533.

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Ewald, W. B. "Intuitionistic tense and modal logic." Journal of Symbolic Logic 51, no. 1 (March 1986): 166–79. http://dx.doi.org/10.2307/2273953.

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In this article we shall construct intuitionistic analogues to the main systems of classical tense logic. Since each classical modal logic can be gotten from some tense logic by one of the definitions(i) □ p ≡ p ∧ Gp ∧ Hp, ◇p ≡ p ∨ Fp ∨ Pp; or,(ii) □ p ≡ p ∧ Gp, ◇p = p ∨ Fp(see [5]), we shall find that our intuitionistic tense logics give us analogues to the classical modal logics as well.We shall not here discuss the philosophical issues raised by our logics. Readers interested in the intuitionistic view of time and modality should see [2] for a detailed discussion.In §2 we define the Kripke models for IKt, the intuitionistic analogue to Lemmon's system Kt. We then prove the completeness and decidability of this system (§§3–5). Finally, we extend our results to other sorts of tense logic and to modal logic.In the language of IKt, we have: sentence-letters p, q, r, etc.; the (intuitionistic) connectives ∧, ∨, →, ¬; and unary operators P (“it was the case”), F (it will be the case”), H (“it has always been the case”) and G (“it will always be the case”). Formulas are defined inductively: all sentence-letters are formulas; if X is a formula, so are ¬X, PX, FX, HX, and GX; if X and Y are formulas, so are X ∧ Y, X ∨ Y, and X → Y. We shall see that, in contrast to classical tense logic, F and P cannot be defined in terms of G and H.

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Dissertations / Theses on the topic "Modal logic"

1

Wansing, Heinrich. "Displaying modal logic /." Dordrecht [u.a.] : Kluwer, 1998. http://www.gbv.de/dms/ilmenau/toc/24662969X.PDF.

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Papacchini, Fabio. "Minimal model reasoning for modal logic." Thesis, University of Manchester, 2015. https://www.research.manchester.ac.uk/portal/en/theses/minimal-model-reasoning-for-modal-logic(dbfeb158-f719-4640-9cc9-92abd26bd83e).html.

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Model generation and minimal model generation are useful for tasks such as model checking, query answering and for debugging of logical specifications. Due to this variety of applications, several minimality criteria and model generation methods for classical logics have been studied. Minimal model generation for modal logics how ever did not receive the same attention from the research community. This thesis aims to fill this gap by investigating minimality criteria and designing minimal model generation procedures for all the sublogics of the multi-modal logic S5(m) and their extensions with universal modalities. All the procedures are minimal model sound and complete, in the sense that they generate all and only minimal models. The starting point of the investigation is the definition of a Herbrand semantics for modal logics on which a syntactic minimality criterion is devised. The syntactic nature of the minimality criterion allows for an efficient minimal model generation procedure, but, on the other hand, the resulting minimal models can be redundant or semantically non minimal with respect to each other. To overcome the syntactic limitations of the first minimality criterion, the thesis moves from minimal modal Herbrand models to semantic minimality criteria based on subset-simulation. At first, theoretical procedures for the generation of models minimal modulo subset-simulation are presented. These procedures for the generation of models minimal modulo subset-simulation are minimal model sound and complete, but they might not terminate. The minimality criterion and the procedures are then refined in such a way that termination can be ensured while preserving minimal model soundness and completeness.

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Batchelor, Roderick. "Investigations in modal logic." Thesis, King's College London (University of London), 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.409258.

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Wilkinson, Toby. "Enriched coalgebraic modal logic." Thesis, University of Southampton, 2013. https://eprints.soton.ac.uk/354112/.

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We formalise the notion of enriched coalgebraic modal logic, and determine conditions on the category V (over which we enrich), that allow an enriched logical connection to be extended to a framework for enriched coalgebraic modal logic. Our framework uses V-functors L: A → A and T: X → X, where L determines the modalities of the resulting modal logics, and T determines the coalgebras that provide the semantics. We introduce the V-category Mod(A, α) of models for an L-algebra (A, α), and show that the forgetful V-functor from Mod(A, α) to X creates conical colimits. The concepts of bisimulation, simulation, and behavioural metrics (behavioural approximations),are generalised to a notion of behavioural questions that can be asked of pairs of states in a model. These behavioural questions are shown to arise through choosing the category V to be constructed through enrichment over a commutative unital quantale (Q, Ⓧ, I) in the style of Lawvere (1973). Corresponding generalisations of logical equivalence and expressivity are also introduced,and expressivity of an L-algebra (A, α) is shown to have an abstract category theoretic characterisation in terms of the existence of a so-called behavioural skeleton in the category Mod(A, α). In the resulting framework every model carries the means to compare the behaviour of its states, and we argue that this implies a class of systems is not fully defined until it is specified how states are to be compared or related.

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Murakami, Yuko. "Modal logic of partitions." [Bloomington, Ind.] : Indiana University, 2005. http://wwwlib.umi.com/dissertations/fullcit/3162977.

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Thesis (Ph.D.)--Indiana University, Dept. of Philosophy, 2005.
Title from PDF t.p. (viewed Dec. 2, 2008). Source: Dissertation Abstracts International, Volume: 66-02, Section: A, page: 0620. Chairs: Lawrence Moss; Michael Dunn.

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Zanichelli, Riccardo <1993&gt. "Aristotle’s modal syllogistic and first-order modal logic." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2022. http://amsdottorato.unibo.it/10396/1/rzamsafml.pdf.

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In Prior Analytics 1.1–22, Aristotle develops his proof system of non-modal and modal propositions. This system is given in the language of propositions, and Aristotle is concerned with establishing some properties and relations that the expressions of this language enjoy. However, modern scholarship has found some of his results inconsistent with positions defended elsewhere. The set of rules of inference of this system has also caused perplexity: there does not seem to be a single interpretation that validates all the rules which Aristotle is explicitly committed to using in his proofs. Some commentators have argued that these and other problems cannot be successfully addressed from the viewpoint of the traditional, ‘first-order’ interpretation of Aristotle’s syllogistic, whereby propositions are taken to involve quantification over individuals only. Accordingly, this interpretation not only is inadequate for formal analysis, but also stems from a misunderstanding of Aristotle’s ideas about quantification. On the contrary, in this study I purport to vindicate the adequacy and plausibility of the first-order interpretation. Together with some assumptions about the language of propositions and an appropriate regimentation, the first-order interpretation yields promising solutions to many of the problems raised by the modal syllogistic. Thus, I present a reconstruction of the language of propositions and a formal interpretation thereof which will prove respectful and responsive to most of the views endorsed by Aristotle in the ‘modal’ chapters of the Analytics.

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Thalmann, Lars. "Term-modal logic and quantifier-free dynamic assignment logic." Doctoral thesis, Uppsala : Institutionen för informationsteknologi, Univ. [distributör], 2000. http://publications.uu.se/theses/91-506-1443-6/.

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Chou, Soi Ngan. "Normal systems of modal logic." Thesis, University of Macau, 2000. http://umaclib3.umac.mo/record=b1446655.

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Martin, Alan J. "Modal and fixpoint linear logic." Thesis, University of Ottawa (Canada), 2002. http://hdl.handle.net/10393/6074.

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This thesis provides adaptations of the algebraic and relational semantics of modal logic to model J.-Y. Girard's linear logic extended with general modalities. This work extends the work of M. D'Agostino, D. Gabbay, and A. Russo on modalities in implication systems, which include a fragment of linear logic, and the work of J.-Y. Girard on phase semantics for linear logic. We develop deductive systems based on the Gentzen-style sequent calculi of Ohnishi and Matsumoto and the indexed sequents of Mints, and prove cut-elimination properties. We show that semantics and deductive systems that are equivalent for classical modal logic become nonequivalent when adapted to linear logic. We also provide a semantics based on Girard's phase semantics for the fixpoint operators of the modal mu-calculus, developed by D. Kozen, E. A. Emerson, E. Clarke, and others, in linear logic, and consider the translation of Y. Lafont's exponentials with the Free Storage rule into linear logic with fixpoint operators.

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Costa, Marcos Mota do Carmo. "Characterization of modal (action) logic." Thesis, Imperial College London, 1990. http://hdl.handle.net/10044/1/47821.

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Books on the topic "Modal logic"

1

Girle, Rod. Modal logics and philosophy: Introduction to modal logic. Teddington: Acumen, 2000.

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Chagrov, Alexander. Modal logic. Oxford: Clarendon Press, 1997.

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Wansing, Heinrich. Displaying Modal Logic. Dordrecht: Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-017-1280-4.

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Introductory modal logic. Notre Dame, Ind: University of Notre Dame Press, 1986.

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Rijke, Maarten de. Extending modal logic. Amsterdam: Institute for Logic, Language and Computation,Universiteit van Amsterdam, 1993.

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Wansing, H. Displaying modal logic. Dordrecht [Netherlands]: Kluwer Academic, 1998.

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Maarten, Marx, Pólos László, and Masuch Michael 1949-, eds. Arrow logic and multi-modal logic. Stanford, Calif: CSLI Publications, 1996.

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Eijck, J. van. Dynamic modal predicate logic. Utrecht: Research Institute for Language and Speech, 1993.

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Marx, Maarten, and Yde Venema. Multi-Dimensional Modal Logic. Dordrecht: Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-011-5694-3.

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Ruzsa, Imre. Modal Logic with Descriptions. Dordrecht: Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-017-2294-0.

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Book chapters on the topic "Modal logic"

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Wansing, Heinrich. "Display Logic." In Displaying Modal Logic, 27–46. Dordrecht: Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-017-1280-4_3.

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Nerode, Anil, and Richard A. Shore. "Modal Logic." In Logic for Applications, 221–62. New York, NY: Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4612-0649-1_5.

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de Swart, H. C. M. "Modal Logic." In Springer Undergraduate Texts in Philosophy, 277–328. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-03255-5_6.

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Chatti, Saloua. "Modal Logic." In Studies in Universal Logic, 147–262. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-27466-5_4.

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Nerode, Anil, and Richard A. Shore. "Modal Logic." In Logic for Applications, 207–45. New York, NY: Springer US, 1993. http://dx.doi.org/10.1007/978-1-4684-0211-7_4.

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Gochet, Paul. "Modal logic." In Handbook of Pragmatics, 1–9. Amsterdam: John Benjamins Publishing Company, 2007. http://dx.doi.org/10.1075/hop.11.mod1.

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Gochet, Paul. "Modal logic." In Handbook of Pragmatics, 371–76. Amsterdam: John Benjamins Publishing Company, 1995. http://dx.doi.org/10.1075/hop.m.mod1.

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Gochet, Paul. "Modal logic." In Philosophical Perspectives for Pragmatics, 163–70. Amsterdam: John Benjamins Publishing Company, 2011. http://dx.doi.org/10.1075/hoph.10.14goc.

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Gochet, Paul. "Modal logic." In Handbook of Pragmatics, 954–60. Amsterdam: John Benjamins Publishing Company, 2022. http://dx.doi.org/10.1075/hop.m2.mod1.

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Marek, V. Wiktor, and Mirosław Truszczyński. "Modal logic." In Artificial Intelligence, 189–222. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-662-02906-0_7.

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Conference papers on the topic "Modal logic"

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Calcagno, Cristiano, Philippa Gardner, and Uri Zarfaty. "Context logic as modal logic." In the 34th annual ACM SIGPLAN-SIGACT symposium. New York, New York, USA: ACM Press, 2007. http://dx.doi.org/10.1145/1190216.1190236.

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Wild, Paul, and Lutz Schröder. "A Characterization Theorem for a Modal Description Logic." In Twenty-Sixth International Joint Conference on Artificial Intelligence. California: International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/181.

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Modal description logics feature modalities that capture dependence of knowledge on parameters such as time, place, or the information state of agents. E.g., the logic S5-ALC combines the standard description logic ALC with an S5-modality that can be understood as an epistemic operator or as representing (undirected) change. This logic embeds into a corresponding modal first-order logic S5-FOL. We prove a modal characterization theorem for this embedding, in analogy to results by van Benthem and Rosen relating ALC to standard first-order logic: We show that S5-ALC with only local roles is, both over finite and over unrestricted models, precisely the bisimulation-invariant fragment of S5-FOL, thus giving an exact description of the expressive power of S5-ALC with only local roles.

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Esteva, Francese, Lluis Godo, and Ricardo Oscar Rodriguez. "On the relation between modal and multi-modal logics over Łukasiewicz logic." In 2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE). IEEE, 2017. http://dx.doi.org/10.1109/fuzz-ieee.2017.8015703.

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Kamide, Norihiro. "Self-extensional Paradefinite Four-valued Modal Logic Compatible with Standard Modal Logic." In 2023 IEEE 53rd International Symposium on Multiple-Valued Logic (ISMVL). IEEE, 2023. http://dx.doi.org/10.1109/ismvl57333.2023.00017.

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Mizutani, Kaori, and Takamasa Akiyama. "A Logit Model for Modal Choice with a Fuzzy Logic Utility Function." In Second International Conference on Transportation and Traffic Studies (ICTTS ). Reston, VA: American Society of Civil Engineers, 2000. http://dx.doi.org/10.1061/40503(277)49.

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Kumar, Pradeep. "Modal logic & ownership types." In Companion to the 21st ACM SIGPLAN conference. New York, New York, USA: ACM Press, 2006. http://dx.doi.org/10.1145/1176617.1176721.

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Yang, Syraya Chin-mu. "A UNIVERSALLY FREE MODAL LOGIC." In The 11th Asian Logic Conference - In Honor of Professor Chong Chitat on His 60th Birthday. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814360548_0010.

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Hong, Zhiling. "Constrained Epistemic Action Modal Logic." In Next Generation Computer and Information Technology 2015. Science & Engineering Research Support soCiety, 2015. http://dx.doi.org/10.14257/astl.2015.111.21.

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KRAUSE, DÉCIO, JONAS R. BECKER ARENHART, and PEDRO MERLUSSI. "A MODAL LOGIC OF INDISCERNIBILITY." In Quantum Mechanics and Quantum Information: Physical, Philosophical and Logical Approaches. WORLD SCIENTIFIC, 2016. http://dx.doi.org/10.1142/9789813146280_0011.

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Jiang, Min, Yang Yu, Fei Chao, Minghui Shi, and Changle Zhou. "A connectionist model for 2-dimensional modal logic." In 2013 IEEE Symposium on Computational Intelligence for Human-like Intelligence (CIHLI). IEEE, 2013. http://dx.doi.org/10.1109/cihli.2013.6613265.

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Reports on the topic "Modal logic"

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Lutz, Carsten, and Ulrike Sattler. The Complexity of Reasoning with Boolean Modal Logics (Extended Version). Aachen University of Technology, 1999. http://dx.doi.org/10.25368/2022.105.

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Since Modal Logics are an extension of Propositional Logic, they provide Boolean operators for constructing complex formulae. However, most Modal Logics do not admit Boolean operators for constructing complex modal parameters to be used in the box and diamond operators. This asymmetry is not present in Boolean Modal Logics, in which box and diamond quantify over arbitrary Boolean combinations of atomic model parameters.

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Lutz, Carsten, and Frank Wolter. Modal Logics of Topological Relations. Technische Universität Dresden, 2004. http://dx.doi.org/10.25368/2022.142.

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The eight topological RCC8(or Egenhofer-Franzosa)- relations between spatial regions play a fundamental role in spatial reasoning, spatial and constraint databases, and geographical information systems. In analogy with Halpern and Shoham’s modal logic of time intervals based on the Allen relations, we introduce a family of modal logics equipped with eight modal operators that are interpreted by the RCC8-relations. The semantics is based on region spaces induced by standard topological spaces, in particular the real plane. We investigate the expressive power and computational complexity of the logics obtained in this way. It turns our that, similar to Halpern and Shoham’s logic, the expressive power is rather natural, but the computational behavior is problematic: topological modal logics are usually undecidable and often not even recursively enumerable. This even holds if we restrict ourselves to classes of finite region spaces or to substructures of region spaces induced by topological spaces. We also analyze modal logics based on the set of RCC5relations, with similar results.

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Hirsch, Colin, and Stephan Tobies. A Tableau Algorithm for the Clique Guarded Fragment. Aachen University of Technology, 1999. http://dx.doi.org/10.25368/2022.106.

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Aus der Einleitung: The Guarded Fragment of first-order logic, introduced by Andréka, van Benthem, and Németi, has been a succesful attempt to transfer many good properties of modal, temporal, and description logics to a larger fragment of predicate logic. Among these are decidability, the finite modal property, invariance under an appropriate variant of bisimulation, and other nice modal theoretic properties.

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Lutz, Carsten, and Dirk Walther. PDL with Negation of Atomic Programs. Technische Universität Dresden, 2003. http://dx.doi.org/10.25368/2022.129.

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Propositional dynamic logic (PDL) is one of the most succesful variants of modal logic. To make it even more useful for applications, many extensions of PDL have been considered in the literature. A very natural and useful such extension is with negation of programs. Unfortunately, it is long-known that reasoning with the resulting logic is undecidable. In this paper, we consider the extension of PDL with negation of atomic programs, only. We argue that this logic is still useful, e.g. in the context of description logics, and prove that satisfiability is decidable and EXPTIME-complete using an approach based on Büchi tree automata.

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Kozachenko, Nadiia. AGM cognitive actions as modal operators of three-valued logic: presentation. Ruhr-Universität Bochum, July 2022. http://dx.doi.org/10.31812/123456789/6687.

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AGM is designed so that its principles can be applied to the development of belief dynamics models, regardless of the field of application. The main idea of this work is to see how we can to represent cognitive actions considered in AGM within a certain three-valued logic, and check what interesting properties can be discovered in this way. To do this, we will consider the basic concepts and principles of AGM. Then we interpret them in a logical schema. And then we see what information about them we can get in the resulting system.

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Baader, Franz, Stefan Borgwardt, and Barbara Morawska. Computing Minimal EL-Unifiers is Hard. Technische Universität Dresden, 2012. http://dx.doi.org/10.25368/2022.187.

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Unification has been investigated both in modal logics and in description logics, albeit with different motivations. In description logics, unification can be used to detect redundancies in ontologies. In this context, it is not sufficient to decide unifiability, one must also compute appropriate unifiers and present them to the user. For the description logic EL, which is used to define several large biomedical ontologies, deciding unifiability is an NP-complete problem. It is known that every solvable EL-unification problem has a minimal unifier, and that every minimal unifier is a local unifier. Existing unification algorithms for EL compute all minimal unifiers, but additionally (all or some) non-minimal local unifiers. Computing only the minimal unifiers would be better since there are considerably less minimal unifiers than local ones, and their size is usually also quite small. In this paper we investigate the question whether the known algorithms for EL-unification can be modified such that they compute exactly the minimal unifiers without changing the complexity and the basic nature of the algorithms. Basically, the answer we give to this question is negative.

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Borgwardt, Stefan, Felix Distel, and Rafael Peñaloza. Gödel Description Logics: Decidability in the Absence of the Finitely-Valued Model Property. Technische Universität Dresden, 2013. http://dx.doi.org/10.25368/2022.199.

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In the last few years there has been a large effort for analysing the computational properties of reasoning in fuzzy Description Logics. This has led to a number of papers studying the complexity of these logics, depending on their chosen semantics. Surprisingly, despite being arguably the simplest form of fuzzy semantics, not much is known about the complexity of reasoning in fuzzy DLs w.r.t. witnessed models over the Gödel t-norm. We show that in the logic G-IALC, reasoning cannot be restricted to finitely valued models in general. Despite this negative result, we also show that all the standard reasoning problems can be solved in this logic in exponential time, matching the complexity of reasoning in classical ALC.

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Borgwardt, Stefan, and Rafael Peñaloza. Consistency in Fuzzy Description Logics over Residuated De Morgan Lattices. Technische Universität Dresden, 2012. http://dx.doi.org/10.25368/2022.188.

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Fuzzy description logics can be used to model vague knowledge in application domains. This paper analyses the consistency and satisfiability problems in the description logic SHI with semantics based on a complete residuated De Morgan lattice. The problems are undecidable in the general case, but can be decided by a tableau algorithm when restricted to finite lattices. For some sublogics of SHI, we provide upper complexity bounds that match the complexity of crisp reasoning.

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Conte, Ianina. Evidence Synthesis Programme (ESP) Logic Model. National Institute for Health and Care Research, February 2023. http://dx.doi.org/10.3310/nihropenres.1115203.1.

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Davoren, Jennifer M. Modal Logics for Continuous Dynamics. Fort Belvoir, VA: Defense Technical Information Center, November 1997. http://dx.doi.org/10.21236/ada344316.

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