Abstract
The categorical point of view in logic tries to understand the meaning of all the connectives and operators in a structural, conceptual way as opposed to the purely descriptive point of view. What is in question is the explanation of the linguistic phenomena that is not reduced to a mere description, say, of the logical laws that hold or do not hold in a given context. For questions related to philosophy the intuitive appeal to the natural language is fundamental, but we also feel that some motivations and methods of other nature might be needed too, for instance in order to produce systems able to originate satisfactory mathematical research, as happens in the propositional case for the main non-classical logics. This is what we are trying in this paper to do for quantified modal logic: we basically review the material of Ghilardi/Meloni (1988), (1991a), (1991b), by stressing the conceptual methods which made the investigations themselves possible and by emphasizing the philosophical applications that arose almost immediately after the main key points about substitution became clear. On the other hand, readers more interested in the original mathematical motivations and results are referred to the above-mentioned papers.
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References
Berta, C./Meloni, Giancarlo (1987): “Dottrine con comprensione e logiche libere”, in Atti degli incontri di logica matematicavol.3, Siena: Università di Siena, 177–185.
Corsi, Giovanna/Ghilardi, Silvio (1992): “Semantical Aspects of Quantified Modal Logic”, in Cristina Bicchieri, Maria Luisa Chiara Dalla, eds., Knowledge, Belief and Strategic Interaction, Cambridge: Cambridge University Press, 167–196.
Ghilardi, Silvio (1990): Modalità e Categorie,Tesi di dottorato in Matematica (Università di Milano).
Ghilardi, Silvio (1991): “Incompleteness Results in Kripke Semantics”, in The Journal of Symbolic Logic 56 [2], 517–538.
Ghilardi, Silvio (1992): “Quantified Extensions of Propositional Intermediate Logics ”, in Studia Logica 51, 195–214.
Ghilardi, Silvio/Meloni, Giancarlo (1988): “Modal and Tense Predicate Logic: Models in Presheaves and Categorical Conceptualization ”, in Francis Borceux, ed. Categorical Algebra and its ApplicationsBerlin-New York: Springer [= Springer LNM 1348], 130–142.
Ghilardi, Silvio/Meloni, Giancarlo (1991a): “Philosophical and Mathematical Investigations in First Order Modal Logic”, in Gabriele Usberti, ed. Problemi fondazionali in teoria del significato — Atti del convegno di PontignanoFirenze: Olsckhi, 77–107.
Ghilardi, Silvio/Meloni, Giancarlo (199 lb): “Relational and Topological Semantics for Temporal and Modal Predicative Logics”, in Giovanna Corsi, Giovanni Sambin, eds., Nuovi problemi della logica e della filosofia della scienza, vol.2, Bologna: CLUEB, 59–77.
Ghilardi, Silvio/Meloni, Giancarlo (1996): “Relational and Partial Variable Sets and Basic Predicate Logic ”, in The Journal of Symbolic Logic 61 [3], 843–872.
Hintikka, Jaakko (1970): “Existential Presuppositions and Uniqueness Presuppositions ”, in Karel Lambert, ed. Philosophical Problems in Logic. Some Recent DevelopmentsDordrecht: Reidel, 20–55.
Lawvere, F. William (1969): “Adjointness in Foundations”, in Dialectica 23 [3/4], 281–296.
Lawvere, F. William (1970): “Equality in Hyperdoctrines and Comprehension Schema as an Adjoint Functor”, in Alex Heller, ed. Applications of Categorical Algebra Proc. of Symp. in Pure Math. AMSvol.17, 1–14.
Makkai, Michael/Reyes, Gonzalo E. (1977): First Order Categorical Logic. Model-Theoretical Methods in the Theory of Topoi and Related Categories, Berlin-Heidelberg-New York: Springer [= Springer LNM 611].
Makkai, Michael/Reyes, Gonzalo E. (1997): “Completeness Results for Intuitionistic and Modal Logic in a Categorical Setting”, in Annals of Pure and Applied Logic 72, 25–101.
Stalnaker, Robert C./Thomason, Richmond H. (1968): “Abstraction in First-Order Modal Logic”, in Theoria 14 [3], 203–207.
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Ghilardi, S. (2001). Substitution, Quantifiers and Identity in Modal Logic. In: Morscher, E., Hieke, A. (eds) New Essays in Free Logic. Applied Logic Series, vol 23. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9761-6_5
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DOI: https://doi.org/10.1007/978-94-015-9761-6_5
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