Abstract
This paper sets out a philosophical interpretation of the model theory of Mares and Goldblatt (The Journal of Symbolic Logic 71, 2006). This interpretation distinguishes between truth conditions and information conditions. Whereas the usual Tarskian truth condition holds for universally quantified statements, their information condition is quite different. The information condition utilizes general propositions. The present paper gives a philosophical explanation of general propositions and argues that these are needed to give an adequate theory of general information.
Similar content being viewed by others
References
Ambrose A. (1985). Mathematical generality. In: Lazerowitz, M. and Ambrose, A. (eds) Necessity and language, pp 101–120. Croom Helm, London
Anderson A.R., Belnap N.D. and Dunn J.M. (1992). Entailment: Logic of relevance and necessity (Vol. II). Princeton University Press, Princeton
Armstrong D.M. (1989). A combinatorial theory of possibility. Cambridge University Press, Cambridge
Armstrong D.M. (1997). A world of states of affairs. Cambridge University Press, Cambridge
Armstrong D.M. (2004). Truth and truthmakers. Cambridge University Press, Cambridge
Barwise J. (1993). Constraints, channels and the flow of information. In: Aczel, P., Israel, D., Katagiri, Y., and Peters, S. (eds) Situation theory and its applications Vol. 3, pp 3–27. Stanford, CSLI
Barwise J. and Etchemendy J. (1987). The liar. Oxford University Press, Oxford
Barwise J. and Perry J. (1983). Situations and attitudes. MIT Press, Cambridge, MA
Bratko I. (1986). Prolog programming for artificial intelligence. Addison-Wesley, Workingham, UK
Dunn J.M. (1993). Star and perp. Philosophical Perspectives 7: 331–357
Fine K. (1988). Semantics for quantified relevant logic. Journal of Philosophical Logic 17: 27–59. Reprinted in Anderson et al. (1992) § 53
Fine K. (1989). Incompleteness of quantified relevance logics. In: Norman, J. and Sylvan, R. (eds) Directions in relevant logic, pp. Kluwer, Dordrecht
Goldblatt, R., & Hodkinson, I. (forthcoming). Commutativity of quantifiers in varying-domain Kripke Models. In D. Makinson, J. Malinowksi, & H. Wansing (Eds.), Trends in logic: Towards mathematical philosophy. Heidelberg: Springer.
Goldblatt R. and Mares E.D. (2006). A general semantics for quantified modal logic. In: Gouvenatori, G., Hodkinson, I. and Venema, Y. (eds) Advances in modal logic (Vol. 6), pp 1–1. College Publications, London
Heil J. (2003). From an ontological point of view. Oxford University Press, Oxford
Mares E.D. (2004). Relevant logic: A philosophical interpretation. Cambridge University Press, Cambridge
Mares E.D. (2006). The semantics of denial. In: Brown, B. and Lepage, F. (eds) Truth and probability: Essays in honour of Hughes Leblanc, pp 49–58. College Publications, London
Mares E.D. and Goldblatt R. (2006). An alternative semantics for quantified relevant logic. The Journal of Symbolic Logic 71: 163–187
Restall G. (1996). Information flow and relevant logics. In: Seligman, J. and Westerståhl, D. (eds) Logic, language and computation, pp 463–477. Stanford, CSLI
Russell B.A.W. (1986). The philosophy of logical atomism. In: (eds) Collected papers (Vol. 8), pp 157–244. George Allen and Unwin, London
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mares, E.D. General information in relevant logic. Synthese 167, 343–362 (2009). https://doi.org/10.1007/s11229-008-9412-9
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11229-008-9412-9