Diversification of object-languages for propositional logics. (English) Zbl 1509.03074
Summary: I argue in favour of object languages of logics to be diversely-generated, that is, not having identical (or equivalent) immediate sub-formulas. In addition to diversely-generated object languages constituting a more appropriate abstraction of the use of sentential connectives in natural language, I show that such language lead to a simplifications w.r.t. some specific issues: the identity of proofs, the factual equivalence (in logics of grounding) and the Mingle axiom in relevance logics. I also point out that some of the properties of classical logic based on freely-generated object languagest.
MSC:
| 03B47 | Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) |
| 03B65 | Logic of natural languages |
Keywords:
freely-generated syntax; diversely-generated syntax; Gricean maxims; identity of proof; logics of grounding; relevance logis; self implication; mingleReferences:
| [1] | Ageron, P. (2007). Logic without self-deductibility. In B. Jean-Yves (Eds.), Logica Universalis (2nd edition) (pp. 87-93). Birkhäuser, Basel. https://doi.org/10.1007/978-3-7643-8354-1-5. · Zbl 1143.03341 |
| [2] | Anderson, A. R., & Belnap, N. D. Jr. (1975). Entailment (vol. 1). Princeton University Press: N.J. · Zbl 0323.02030 |
| [3] | Avron, A. (1992). Whither relevance logic. Journal of philosophical Logic, 21(3), 243-281. · Zbl 0773.03015 · doi:10.1007/BF00260930 |
| [4] | Béziau, J-Y. (2012). History of truth-values. In M. G. Dov and W. Woods (Eds), Handbook of the History of Logic (pp 233-305). Elsevier: Amsterdam. Vol. 11 - Logic: a history of its central concepts. · Zbl 1348.03006 |
| [5] | Bloom, S. L., Brown, D. J., & Suszko, R. (1970). Some theorems on abstract logics. Algebra i Logika, 9, 274-280. · Zbl 0225.02042 · doi:10.1007/BF02218674 |
| [6] | Correia, F. (2014). Logical grounds. Review of Symbolic Logic, 7, 31-59. · Zbl 1344.03005 · doi:10.1017/S1755020313000300 |
| [7] | Correia, F. (2016). On the logic of factual equivalence. Review of Symbolic Logic, 9, 103-122. · Zbl 1386.03027 · doi:10.1017/S1755020315000258 |
| [8] | Destouches-Février, P. (1948). Manifestations et sens de la notion de complémentarité. Dialectica, 2, 383-412. · Zbl 0041.35318 · doi:10.1111/j.1746-8361.1948.tb00709.x |
| [9] | Do \[\breve{{\rm s}}\] s˘en, K. (2015). Inferential semantics. In W. Heinrich (Eds), Dag Prawitz on proofs and meaning. Springer International Publishing Switzerland. Outstanding contributions to logic 7. · Zbl 1304.03008 |
| [10] | Fine, Kit (2012). Guide to ground. In Fabrice Correia and Benjamin Schnieder, editors, Metaphysical grounding, pages 37-80. Cambridge University Press, Cambridge. |
| [11] | Grice, H. P. (1975). Logic and conversation. In C. Peter and M. I. Jerry (Eds), Syntax and Semantics 3. Academic Press, New York. |
| [12] | Humberstone, L. (2011). The connectives. Cambridge: MIT Press. · Zbl 1242.03002 |
| [13] | Hurford, J. (1974). Exclusive or inclusive disjunction. Foundations of Language, 11, 409-411. |
| [14] | Kleene, S. C. (1952). Introduction to metamathematics. Amsterdam: North-Holland. · Zbl 0047.00703 |
| [15] | Krämer, S., & Roski, S. (2015). A note on the logic of worldly grounds. Thought, 4, 59-68. |
| [16] | Poggiolesi, F. (2016). On constructing a logic for the notion of complete and immediate formal grounding. Synthese (forthcoming). https://doi.org/10.1007/s11229-016-1265-z. · Zbl 1380.03021 |
| [17] | Poggiolesi, Francesca. (2016). On defining the notion of complete and immediate formal grounding. Synthese, 193, 3147-3167. · Zbl 1380.03021 · doi:10.1007/s11229-015-0923-x |
| [18] | Rabin, Gabriel Oak, & Rabern, Brian. (2016). Well founding grounding grounding. Journal of Philosophical Logic, 45, 349-379. · Zbl 1392.03015 · doi:10.1007/s10992-015-9376-4 |
| [19] | Tiomkin, M. (2013). A sequent calculus for a logic of contingencies. Journal of Applied Logic, 11. · Zbl 1284.03256 |
| [20] | Trogdon, K. (2013). An introduction to grounding. In H. Miguel, S. Benjamin, and S. Alex (Eds), Dependence. Basic Philosophical Concepts, pp 97-122. Philosophia Verlag. |
| [21] | Wansing, H. (2014). Connexive logic. In N. Z. Edward (Ed), The Stanford Encyclopedia of Philosophy. Fall 2014 edition. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
