Some Computational Constraints in Epistemic Logic
| Abstract | Some systems of modal logic, such as S5, which are often used as epistemic logics with the ‘necessity’ operator read as ‘the agent knows that’, are problematic as general epistemic logics for agents whose computational capacity does not exceed that of a Turing machine because they impose unwarranted constraints on the agent’s theory of non-epistemic aspects of the world, for example by requiring the theory to be decidable rather than merely recursively axiomatizable. To generalize this idea, two constraints on an epistemic logic are formulated: r.e. conservativeness, that any recursively enumerable theory R in the sublanguage without the epistemic operator is conservatively extended by some recursively enumerable theory in the language with the epistemic operator which is permitted by the logic to be the agent’s overall theory; the weaker requirement of r.e. quasi-conservativeness is similar except for applying only when R is consistent. The logic S5 is not even r.e. quasiconservative; this result is generalized to many other modal logics. However, it is also proved that the modal logics S4, Grz and KDE are r.e. quasi-conservative and that K4, KE and the provability logic GLS are r.e. conservative. Finally, r.e. conservativeness and r.e. quasiconservativeness are compared with related non-computational constraints. | |||||||||
| Keywords | No keywords specified (fix it) | |||||||||
| Categories | ||||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,705 |
| External links |
  Try with proxy. |
| Through your library | Only published papers are available at libraries |
Similar books and articlesKrystyna Misiuna (2011). O pewnej logice informacji. Filozofia Nauki 1.
Wesley H. Holliday (forthcoming). Epistemic Closure and Epistemic Logic I: Relevant Alternatives and Subjunctivism. Journal of Philosophical Logic.
Dov M. Gabbay (ed.) (2003). Many-Dimensional Modal Logics: Theory and Applications. Elsevier North Holland.
Boudewijn de Bruin (2008). Epistemic Logic and Epistemology. In Vincent F. Hendricks & Duncan Pritchard (eds.), New Waves in Epistemology. Palgrave Macmillan.
Frank Wolter (2000). First Order Common Knowledge Logics. Studia Logica 65 (2):249-271.
Valentin Goranko & Wojciech Jamroga (2004). Comparing Semantics of Logics for Multi-Agent Systems. Synthese 139 (2):241 - 280.
John Symons (2006). Where's the Bridge? Epistemology and Epistemic Logic. Philosophical Studies 128 (1):137 - 167.
Vincent F. Hendricks & John Symons (2006). Where's the Bridge? Epistemology and Epistemic Logic. Philosophical Studies 128 (1):137 - 167.
Cédric Dégremont & Nina Gierasimczuk (2011). Finite Identification From the Viewpoint of Epistemic Update. Information And Computation 209 (3):383-396.
Wesley H. Holliday & Thomas F. Icard (2010). Moorean Phenomena in Epistemic Logic. In Lev Beklemishev, Valentin Goranko & Valentin B. Shehtman (eds.), Advances in Modal Logic 8. College Publications.
Tomohiro Hoshi & Audrey Yap (2009). Dynamic Epistemic Logic with Branching Temporal Structures. Synthese 169 (2):259 - 281.
Analytics
Monthly downloads |
Added to index2010-12-22Total downloads30 ( #40,899 of 549,196 )Recent downloads (6 months)4 ( #19,303 of 549,196 )How can I increase my downloads? |
My notes
Discussion
