Abstract logics, logic maps, and logic homomorphisms
Logica Universalis 1 (2) (2007)
| Abstract | . What is a logic? Which properties are preserved by maps between logics? What is the right notion for equivalence of logics? In order to give satisfactory answers we generalize and further develop the topological approach of [4] and present the foundations of a general theory of abstract logics which is based on the abstract concept of a theory. Each abstract logic determines a topology on the set of theories. We develop a theory of logic maps and show in what way they induce (continuous, open) functions on the corresponding topological spaces. We also establish connections to well-known notions such as translations of logics and the satisfaction axiom of institutions [5]. Logic homomorphisms are maps that behave in some sense like continuous functions and preserve more topological structure than logic maps in general. We introduce the notion of a logic isomorphism as a (not necessarily bijective) function on the sets of formulas that induces a homeomorphism between the respective topological spaces and gives rise to an equivalence relation on abstract logics. Therefore, we propose logic isomorphisms as an adequate and precise notion for equivalence of logics. Finally, we compare this concept with another recent proposal presented in [2]. | |||||||||
| 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: 5,865 |
| External links |
 |
| Through your library | Configure |
Similar books and articlesItala M. Loffredo D'Ottaviano & Hércules de A. Feitosa (2000). Paraconsistent Logics and Translations. Synthese 125 (1/2):77 - 95.
B. Konev, R. Kontchakov, F. Wolter & M. Zakharyaschev (2006). On Dynamic Topological and Metric Logics. Studia Logica 84 (1):129 - 160.
Josep Maria Font & Miquel Rius (2000). An Abstract Algebraic Logic Approach to Tetravalent Modal Logics. Journal of Symbolic Logic 65 (2):481-518.
Diderik Batens (2007). A Universal Logic Approach to Adaptive Logics. Logica Universalis 1 (1):221-242.
Josep M. Font & Ventura Verdú (1989). A First Approach to Abstract Modal Logics. Journal of Symbolic Logic 54 (3):1042-1062.
Steffen Lewitzka & Andreas B. M. Brunner (2009). Minimally Generated Abstract Logics. Logica Universalis 3 (2).
Analytics
Monthly downloads |
Added to index2009-01-28Total downloads23 ( #54,691 of 556,837 )Recent downloads (6 months)1 ( #64,847 of 556,837 )How can I increase my downloads? |
My notes
Discussion
