Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-24T03:48:26.390Z Has data issue: false hasContentIssue false
Series:   Elements in Philosophy and Logic

Logic and Information

Published online by Cambridge University Press:  20 May 2024

Edwin Mares
Edwin Mares
Affiliation:
Te Herenga Waka – Victoria University of Wellington

Summary

This Element looks at two projects that relate logic and information: the project of using logic to integrate, manipulate and interpret information and the proect of using the notion of information to provide interpretations of logical systems. The Element defines 'information' in a manner that includes misinformation and disinformation and uses this general concept of information to provide an interpretation of various paraconsistent and relevant logics. It also integrates these logics into contemporary theories of informational updating, probability theory and (rather informally) some ideas from the theory of the complexity of proofs. The Element assumes some prior knowledge of modal logic and its possible world semantics, but all the other necessary background is provided.
Get access

Keywords

modal logicrelevance logicphilosophy of informationinformation updatingprobability
Type
Element
Information
Series: Elements in Philosophy and Logic
Online ISBN: 9781009466745
Publisher: Cambridge University Press
Print publication: 13 June 2024

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Bibliography

Allo, Patrick. Logical pluralism and semantic information. Journal of Philosophical Logic, 36:659–694, 2007.CrossRefGoogle Scholar
Allwein, Gerard. A qualitative framework for Shannon information theories. In NSPW ’04: Proceedings of the 2004 Workshop on New Securities Paradigms, pages 23–31, 2005.CrossRefGoogle Scholar
Anderson, Alan, Belanp, Nuel D., and Dunn, J. M.. Entailment: Logic of Relevance and Necessity, volume II. Princeton University Press, Princeton, 1992.Google Scholar
Anderson, Alan and Belnap, Nuel D. Entailment: Logic of Relevance and Necessity, volume I. Princeton University Press, Princeton, 1975.Google Scholar
Avron, Arnon. What is relevance logic? Annals of Pure and Applied Logic, 165(1):26–48, 2014.CrossRefGoogle Scholar
Baltag, Alexandru and Smets, Sonja. Conditional doxastic models: A qualitative approach to dynamic belief revision. Electronic Notes in Theoretical Computer Science, 165:5–21, 2006.CrossRefGoogle Scholar
Barwise, Jon. Constraints, channels, and the flow of information. In Aczel, Peter, Israel, David, Katagiri, Yasuhior, and Peters, Stanley, editors, Situation Theory and its Applications, pages 3–28. CSLI Publications, Stanford, 1993.Google Scholar
Barwise, Jon. State spaces, local logics, and non-monotonicity. In de Rijke, Maartin and Moss, Lawrence, editors, Logic, Language and Computation, volume 2, pages 1–20. CSLI, Stanford, 1999.Google Scholar
Barwise, Jon and Perry, John. Situations and Attitudes. MIT Press, Cambridge, MA, 1983.Google Scholar
Barwise, Jon and Seligman, Jeremy. Information Flow: The Logic of Distributed Systems. Cambridge University Press, Cambridge, 2008.Google Scholar
Belnap, Nuel. How a computer should think. In Ryle, G., editor, Contemporary Aspects of Philosophy, pages 30–55. Oriel Press, Stocksfield, 1977.Google Scholar
Belnap, Nuel. A useful 4-valued logic. In Dunn, J. M. and Epstein, G., editors, Modern Uses of Many-Valued Logic, pages 8–37. Reidel, Dordrecht, 1977.Google Scholar
Brady, Ross. A content semantics for quantified relevant logic I. Studia Logica, 47:111–127, 1988.CrossRefGoogle Scholar
Camp, Elisabeth. Why maps are not propositional. In Grzankowski, Alex and Montague, Michelle, editors, Non-Propositional Intentionality, pages 19–45. Oxford University Press, Oxford, 2018.Google Scholar
Carnap, Rudolf and Bar Hillel, Yohoshua. An outline of a theory of semantic information. Technical Report 247, MIT Research Laboratory of Electronics, 1952.Google Scholar
Chellas, Brian. Basic conditional logic. Journal of Philosophical Logic, 4:133–153, 1975.CrossRefGoogle Scholar
Chellas, Brian. Modal Logic: An Introduction. Cambridge University Press, Cambridge and New York, 1980.CrossRefGoogle Scholar
Clark, Andy and Chalmers, David. The extended mind. Analysis, 58:7–19, 1998.CrossRefGoogle Scholar
Cook, Stephen A. and Reckhow, Robert A.. The relative efficiency of propositional proof systems. The Journal of Symbolic Logic, 44:36–50, 1979.CrossRefGoogle Scholar
Cresswell, M.J.. Structured Meanings. MIT Press, Cambridge, MA, 1985.Google Scholar
Dienes, Zoltan and Perner, Josef. A theory of implicit and explicit knowledge. Behavioral and Brain Sciences, 22:735–808, 1999.CrossRefGoogle Scholar
Došen, Kosta. Sequent systems and groupoid models. II. Studia Logica, 48:41–65, 1989.CrossRefGoogle Scholar
Dretske, Fred. Knowledge and the Flow of Information. MIT Press, Cambridge, MA, 1981.Google Scholar
Michael Dunn, J.. Star and perp. Philosophical Perspectives, 7:331–357, 1993.CrossRefGoogle Scholar
Michael Dunn, J.. The concept of information and the development of modern logic. In Stelzner, W. and Stoeckler, M., editors, Zwischen traditioneller und moderner Logik: Nichtklassiche Ansätze, pages 423–447. Mentis Verlag GmbH, Paderborn, 2001.Google Scholar
Michael Dunn, J.. Contradictory information: Too much of a good thing. Journal of Philosophical Logic, 39:425–452, 2010.CrossRefGoogle Scholar
Michael Dunn, J.. Natural language versus formal language. In Omori, Hitoshi and Wansing, Heinrich, editors, New Essays on Belnap-Dunn Logic, pages 13–20. Springer Verlag, Cham, Switzerland, 2019. Originally presented at an American Philosophical Association meeting in 1968.CrossRefGoogle Scholar
Michael Dunn, J. and Kiefer, Nicholas M.. Contradictory information: Better than nothing? the paradox of the two firefighters. In Başkent, Can and Ferguson, Thomas Macaulay, editors, Graham Priest on Dialetheism and Paraconsistency, pages 231–247. Springer Verlag, 2019.CrossRefGoogle Scholar
Estrada-González, Luis. Complement-topoi and dual intuitionistic logic. Australasian Journal of Logic, 9:26–44, 2010.Google Scholar
Floridi, Luciano, editor. Philosophy of Computing and Information. Blackwell, Oxford, 2004.Google Scholar
Floridi, Luciano. The logic of being informed. Logique et analyse, 196:433–460, 2006.Google Scholar
Floridi, Luciano. The Philosophy of Information. Oxford University Press, Oxford, 2013.Google Scholar
Frege, Gottlob. On sense and reference. The Philosophical Review, 57:209–230, 1948.CrossRefGoogle Scholar
Fuhrmann, André. Theory contraction through base contraction. Journal of Philosophical Logic, 20(2):175–203, 1991.CrossRefGoogle Scholar
Gärdenfors, P.. Knowledge in Flux. Modelling the Dynamics of Epistemic States. MIT Press, 1988.Google Scholar
Gärdenfors, Peter and Makinson, David. Revisions of knowledge systems using epistemic entrenchment. In Vardi, Moshe, editor, Proceedings of the Second Conference on Theoretical Aspects of Reasoning about Knowledge, pages 83–95. Morgan Kaufmann, 1988.Google Scholar
James, J. Gibson. The Ecological Approach to Visual Perception. Psychology Press, New York, 2015. Originally published in 1979.Google Scholar
Goldblatt, Robert. Semantic analysis of orthologic. Journal of Philosophical Logic, 3:19–35, 1974.CrossRefGoogle Scholar
Goldblatt, Robert. Logics of Time and Computation. CSLI Publications, 1992.Google Scholar
Grice, Paul. Studies in the Way of Words. Harvard University Press, Cambridge, MA, 1989.Google Scholar
Hintikka, Jaakko. Logic, Language-Games and Information: Kantian Themes in the Philosophy of Logic. Oxford, England: Oxford, Clarendon Press, 1973.Google Scholar
Humberstone, I. L.. Operational semantics for positive R. Notre Dame Journal of Formal Logic, 29:61–80, 1987.CrossRefGoogle Scholar
Jaśkowski, Stanisław. Rachunek zdań dla systemów dedukcyjnych sprzecznych. Studia Soc. Scient. Torunensis, 1:57–77, 1948.Google Scholar
Jaśkowski, Stanisław. O koniunkcji dyskusyjnej w rachunku zdań dla systemów dedukcyjnych sprzecznych. Studia Soc. Scient. Torunensis, 1:171–172, 1949.Google Scholar
Jaśkowski, Stanisław. Propositional calculus for contradictory deductive systems. Studia Logica, 24:143–160, 1969. Originally presented in 1948.CrossRefGoogle Scholar
Jeffrey, C. King. The Nature and Structure of Content. Oxford University Press, Oxford, 2007.Google Scholar
Krajíček, Jan. Proof Complexity. Cambridge University Press, Cambridge, 2019.CrossRefGoogle Scholar
Kratzer, Angelika. An investigation of the lumps of thought. Linguistics and Philosophy, 12:607–653, 1989.CrossRefGoogle Scholar
Frederick, W. Kroon. Causal descriptivism. Australasian Journal of Philosophy, 65:1–17, 1987.Google Scholar
Lewis, C.I. and Langford, C.H.. Symbolic Logic. Dover, New York, second edition, 1959.Google Scholar
Linsky, Leonard. Oblique Contexts. University of Chicago Pres, Chicago, 1983.Google Scholar
Allen Logan, Shay. Depth relevance and hyperformalism. Journal of Philosophical Logic, 51:721–737, 2022.CrossRefGoogle Scholar
Maddy, Penelope. Second Philosophy. Oxford University Press, Oxford, 2007.CrossRefGoogle Scholar
Mares, Edwin. A star-free semantics for R. Journal of Symbolic Logic, 60:579–590, 1995.CrossRefGoogle Scholar
Mares, Edwin. Relevant Logic: A Philosophical Interpretation. Cambridge University Press, 2004.CrossRefGoogle Scholar
Mares, Edwin. Relevant logic, probabilistic information, and conditionals. Logique et analyse, 49:399–411, 2006.Google Scholar
Mares, Edwin. General information in relevant logic. Synthese, 167:343–362, 2009.CrossRefGoogle Scholar
Mares, Edwin. Belief revision, probabilism, and logic choice. Review of Symbolic Logic, 7(4):647–670, 2014.CrossRefGoogle Scholar
Mares, Edwin and Fuhrmann, André. A relevant theory of conditionals. Journal of Philosophical Logic, 24:645–665, 1995.CrossRefGoogle Scholar
Mares, Edwin, Seligman, Jeremy, and Restall, Greg. Situations, constraints, and channels. In van Benthem, Johan and ter Meulen, Alice G.B., editors, Handbook of Logic and Language, pages 329–344. Elsevier, Amsterdam, 2010.Google Scholar
Martinez, Maricarmen and Sequoiah-Grayson, Sebastian. Logic and Information. In Edward, N. Zalta, editor, The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University, Spring 2019 edition, 2019.Google Scholar
Manuel, A. Martins and Sedlár, Igor, editors. Dynamic Logic: New Trends and Applications, Cham, 2020. Springer Verlag.Google Scholar
Mortensen, Chris. Inconsistent Mathematics. Kluwer, Dordrecht, 1995.CrossRefGoogle Scholar
Nelson, Ruth. What is a secret and what does it have to do with computer security? In Proceedings of the 1994 Workshop on New Securities Paradigms, pages 74–79, 1994.Google Scholar
Ono, Hiroakira. Semantics for substructural logics. In Došen, Kosta and Schröder-Heister, Peter, editors, Substructural Logics, pages 259–291. Oxford University Press, Oxford, 1993.CrossRefGoogle Scholar
Paoli, Francesco. Substructural Logics: A Primer. Springer Verlag, Dordrecht, 2002.CrossRefGoogle Scholar
Parikh, Rohit. Knowledge and the problem of logical omniscience. In Ras, Zibignew and Zemankova, Maria, editors, Proceedings of the Second International Symposium on Intelligent Systems, pages 432–439. North Holland, Amsterdam, 1989.Google Scholar
Pratt, Vaughan. Semantical considerations on the Floyd-Hoare logic. Proceedings of the 17th Annual IEEE Symposium on Foundations of Computer Science, 1976.Google Scholar
Priest, Graham. An Introduction to Non-Classical Logic: From If to Is. Cambridge University Press, Cambridge, second edition, 2008.CrossRefGoogle Scholar
Priest, Graham. Logical theory choice. Australasian Journal of Logic, 16:283–297, 2019.CrossRefGoogle Scholar
Punčochář, Vit, Sedlár, Igor, and Tedder, Andrew. Relevant propositional dynamic logic. Synthese, 3001 forthcoming.Google Scholar
Read, Stephen. Necessary truth and proof. Kriterion: Journal of Philosophy, 51:47–67, 2010.CrossRefGoogle Scholar
Restall, Greg. Four-valued semantics for relevant logics (and some of their rivals). Journal of Philosophical Logic, 24(2):139–160, 1995.CrossRefGoogle Scholar
Restall, Greg. Information flow and relevant logics. In Seligman, Jeremy and Westerstøahl, Dag, editors, Logic, Language and Computation, pages 463–477. CSLI Publications, Stanford, 1995.Google Scholar
Restall, Greg. Negation in relevant logics (how i stopped worrying and learned to love the Routley star). In Gabbay, Dov and Wansing, Heinrich, editors, What is Negation?, pages 53–76. Kluwer Academic Publishers, 1999.CrossRefGoogle Scholar
Routley, Richard and Robert, K. Meyer. Semantics for entailment. In Leblanc, Hughes, editor, Truth, Syntax, and Modality. North Holland, Amsterdam, 1973.Google Scholar
Routley, Richard, Meyer, Robert K., Brady, Ross, and Plumwood, Val. Relevant Logics and their Rivals. Ridgeview, Atascardero, 1983.Google Scholar
Routley, Richard and Routley, Val. The semantics of first-degree entailment. Noûs, 6:335–395, 1972.CrossRefGoogle Scholar
Russell, Bertrand. The Philosophy of Logical Atomism. Open Court, La Salle, IL, 1985.Google Scholar
Russell, Gillian. The justification of the basic laws of logic. Journal of Philosophical Logic, 44:793–803, 2015.CrossRefGoogle Scholar
Schotch, Peter and Jennings, Raymond. On detonating. In Priest, G., Routley, R., and Norman, J., editors, Paraconsistent Logic, pages 306–327. Philosophia Verlag, Munich, 1989.CrossRefGoogle Scholar
Segerberg, Krister. Notes on conditional logic. Studia Logica, 48:157–168, 1989.CrossRefGoogle Scholar
Seligman, Jeremy. Perspectives: A Relativistic Approach to the Theory of Information. PhD thesis, University of Edinburgh, 1990.Google Scholar
Sequoias-Grayson, Sebastian. The scandal of deduction: Hintikka on the information yield of deductive inferences. Journal of Philosophical Logic, 37:67–94, 2008.CrossRefGoogle Scholar
Shannon, Claude E. and Weaver, Warren. The Mathematical Theory of Communication. University of Illinois Press, Champaign, IL, 1963.Google Scholar
Sperber, Dan and Wison, Deirdre. Relevance: Communication and Cognition. Blackwell, Oxford, second edition, 1995.Google Scholar
Tedder, Andrew. Information flow in the vicinity of BB. The Australasian Journal of Logic, 18:1–24, 2021.CrossRefGoogle Scholar
Tedder, Andrew and Bilková, Marta. Relevant propositional dynamic logic. Synthese, 200(3):1–42, 2022.CrossRefGoogle Scholar
van Benthem, Johan. Language in Action: Categories, Lambdas, and Dynamic Logic. MIT Press, Cambridge, MA, 1995.Google Scholar
van Benthem, Johan. Logical Dynamics of Information and Interaction. Cambridge University Press, Cambridge, 2011.CrossRefGoogle Scholar
van Benthem, Johan and Israel, David. Review of Jon Barwise and Jeremy Seligman, Information flow. Journal of Logic, Language, and Information, 8:390–397, 1999.CrossRefGoogle Scholar
Williamson, Timothy. Semantic paradoxes and abductive methodology. In Reflections on the Liar, pages 325–346. Oxford: Oxford University Press, 2017.Google Scholar

Save element to Kindle

To save this element to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Logic and Information
  • Edwin Mares, Te Herenga Waka – Victoria University of Wellington
  • Online ISBN: 9781009466745
Available formats
×

Save element to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Logic and Information
  • Edwin Mares, Te Herenga Waka – Victoria University of Wellington
  • Online ISBN: 9781009466745
Available formats
×

Save element to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Logic and Information
  • Edwin Mares, Te Herenga Waka – Victoria University of Wellington
  • Online ISBN: 9781009466745
Available formats
×