Abstract
We study the logic of comparative concept similarity \(\mathcal{CSL}\) introduced by Sheremet, Tishkovsky, Wolter and Zakharyaschev to capture a form of qualitative similarity comparison. In this logic we can formulate assertions of the form ”objects A are more similar to B than to C”. The semantics of this logic is defined by structures equipped with distance functions evaluating the similarity degree of objects. We consider here the particular case of the semantics induced by minspaces, the latter being distance spaces where the minimum of a set of distances always exists. It turns out that the semantics over arbitrary minspaces can be equivalently specified in terms of preferential structures, typical of conditional logics. We first give a direct axiomatisation of this logic over Minspaces. We next define a decision procedure in the form of a tableaux calculus. Both the calculus and the axiomatisation take advantage of the reformulation of the semantics in terms of preferential structures.
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References
Alenda, R., Olivetti, N., Schwind, C.: Comparative concept similarity over minspaces: Axiomatisation and tableaux calculus. Technical report (2009), http://arxiv.org/abs/0902.0899
Boolos, G.: The Logic of Provability. Cambridge University Press, Cambridge (1993)
Giordano, L., Gliozzi, V., Olivetti, N., Schwind, C.: Tableau calculus for preference-based conditional logics: Pcl and its extensions. ACM Trans. Comput. Log. 10(3) (2009)
Hustadt, U., Tishkovsky, D., Wolter, F., Zakharyaschev, M.: Automated reasoning about metric and topology. In: Fisher, M., van der Hoek, W., Konev, B., Lisitsa, A. (eds.) JELIA 2006. LNCS (LNAI), vol. 4160, pp. 490–493. Springer, Heidelberg (2006)
Kurucz, A., Wolter, F., Zakharyaschev, M.: Modal logics for metric spaces: Open problems. In: Artëmov, S.N., Barringer, H., d’Avila Garcez, A.S., Lamb, L.C., Woods, J. (eds.) We Will Show Them (2), pp. 193–208. College Publications (2005)
Lehmann, D., Magidor, M.: What does a conditional knowledge base entail. Artificial Intelligence 55, 1–60 (1992)
Lewis, D.: Counterfactuals. Basil Blackwell Ltd., Malden (1973)
Nute, D.: Topics in Conditional Logic. Reidel Publishing Company, Dordrecht (1980)
Sheremet, M., Tishkovsky, D., Wolter, F., Zakharyaschev, M.: Comparative similarity, tree automata, and diophantine equations. In: Sutcliffe, G., Voronkov, A. (eds.) LPAR 2005. LNCS, vol. 3835, pp. 651–665. Springer, Heidelberg (2005)
Sheremet, M., Tishkovsky, D., Wolter, F., Zakharyaschev, M.: A logic for concepts and similarity. J. Log. Comput. 17(3), 415–452 (2007)
Sheremet, M., Wolter, F., Zakharyaschev, M.: A modal logic framework for reasoning about comparative distances and topology (submitted, 2008)
Stalnaker, R.: A theory of conditionals. In: Rescher, N. (ed.) Studies in Logical Theory, American Philosophical Quarterly. Monograph Series, vol. 2, pp. 98–112. Blackwell, Oxford (1968)
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Alenda, R., Olivetti, N., Schwind, C. (2009). Comparative Concept Similarity over Minspaces: Axiomatisation and Tableaux Calculus. In: Giese, M., Waaler, A. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2009. Lecture Notes in Computer Science(), vol 5607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02716-1_3
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DOI: https://doi.org/10.1007/978-3-642-02716-1_3
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