Different researchers use "the philosophy of automated theorem p r o v i n g " t o cover d i f f e r e n t concepts, indeed, different levels of concepts. Some w o u l d count such issues as h o w to e f f i c i e n t l y i n d e x databases as part of the philosophy of automated theorem p r o v i n g . Others wonder about whether f o r m u l a s should be represented as strings or as trees or as lists, and call this part of the philosophy of automated theorem p r o v i n g . Yet others concern themselves w i t h what k i n d o f search should b e embodied i n a n y automated theorem prover, or to what degree any automated theorem prover should resemble Prolog. Still others debate whether natural deduction or semantic tableaux or resolution is " b e t t e r " , a n d c a l l t h i s a part of the p h i l o s o p h y of automated theorem p r o v i n g . Some people wonder whether automated theorem p r o v i n g should be " h u m a n oriented" or "machine o r i e n t e d " — sometimes arguing about whether the internal p r o o f methods should be " h u m a n - I i k e " or not, sometimes arguing about whether the generated proof should be output in a f o r m u n d e r s t a n d a b l e by p e o p l e , and sometimes a r g u i n g a b o u t the d e s i r a b i l i t y o f h u m a n intervention in the process of constructing a proof. There are also those w h o ask such questions as whether we s h o u l d even be concerned w i t h completeness or w i t h soundness of a system, or perhaps we should instead look at very efficient (but i n c o m p l e t e ) subsystems or look at methods of generating models w h i c h might nevertheless validate invalid arguments. A n d a l l of these have been v i e w e d as issues in the philosophy of automated theorem proving. Here, I w o u l d l i k e to step back from such i m p l e m e n t - ation issues and ask: " W h a t do we really think we are doing when we w r i t e an automated theorem prover?" My reflections are perhaps idiosyncratic, but I do think that they put the different researchers* efforts into a broader perspective, and give us some k i n d of handle on w h i c h directions we ourselves m i g h t w i s h to pursue when constructing (or extending) an automated theorem proving system. A logic is defined to be (i) a vocabulary and formation rules ( w h i c h tells us w h a t strings of symbols are w e l l - formed formulas in the logic), and ( i i ) a definition of ' p r o o f in that system ( w h i c h tells us the conditions under which an arrangement of formulas in the system constitutes a proof). Historically speaking, definitions of ' p r o o f have been given in various different manners: the most c o m m o n have been H i l b e r t - s t y l e ( a x i o m a t i c ) , Gentzen-style (consecution, or sequent), F i t c h - s t y l e (natural deduction), and Beth-style (tableaux)..
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Connection Tableau Calculi with Disjunctive Constraints.Ortrun Ibens - 2002 - Studia Logica 70 (2):241 - 270.
Automated Theorem Proving for Łukasiewicz Logics.Gordon Beavers - 1993 - Studia Logica 52 (2):183 - 195.
Identity in Modal Logic Theorem Proving.Francis J. Pelletier - 1993 - Studia Logica 52 (2):291 - 308.
Implementing a Relational Theorem Prover for Modal Logic K.Angel Mora, Emilio Munoz Velasco & Joanna Golińska-Pilarek - 2011 - International Journal of Computer Mathematics 88 (9):1869-1884.
An ATP of a Relational Proof System for Order of Magnitude Reasoning with Negligibility, Non-Closeness and Distance.Joanna Golinska-Pilarek, Angel Mora & Emilio Munoz Velasco - 2008 - In Tu-Bao Ho & Zhi-Hua Zhou (eds.), PRICAI 2008: Trends in Artificial Intelligence. Springer. pp. 128--139.
Strategic Construction of Fitch-Style Proofs.Frederic D. Portoraro - 1998 - Studia Logica 60 (1):45-66.
Added to index2010-12-22
Total downloads13 ( #347,264 of 2,153,836 )
Recent downloads (6 months)1 ( #398,274 of 2,153,836 )
How can I increase my downloads?