David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Studia Logica 42 (4):443 - 451 (1983)
Condensed detachment is usually regarded as a notation, and defined by example. In this paper it is regarded as a rule of inference, and rigorously defined with the help of the Unification Theorem of J. A. Robinson. Historically, however, the invention of condensed detachment by C. A. Meredith preceded Robinson's studies of unification. It is argued that Meredith's ideas deserve recognition in the history of unification, and the possibility that Meredith was influenced, through ukasiewicz, by ideas of Tarski going back at least to 1939, and possibly to 1930 or earlier, is discussed. It is proved that a term is derivable by substitution and ordinary detachment from given axioms if and only if it is a substitution instance of a term which is derivable from these axioms by condensed detachment, and it is shown how this theorem enables the ideas of ukasiewicz and Tarski mentioned above to be formalized and extended. Finally, it is shown how condensed detachment may be subsumed within the resolution principle of J. A. Robinson, and several computer studies of particular Hilbert-type propositional calculi using programs based on condensed detachment or on resolution are briefly discussed.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
Stig Kanger (1957). Provability in Logic. Stockholm, Almqvist & Wiksell.
Jeremy George Peterson (1976). Shortest Single Axioms for the Classical Equivalential Calculus. Notre Dame Journal of Formal Logic 17 (2):267-271.
Dag Prawitz (1960). An Improved Proof Procedure. Theoria 26 (2):102-139.
Alfred Tarski (1956). Logic, Semantics, Metamathematics. Oxford, Clarendon Press.
Citations of this work BETA
No citations found.
Similar books and articles
L. Q. English (2007). On the 'Emptiness' of Particles in Condensed-Matter Physics. Foundations of Science 12 (2):155-171.
B. Cornuldeder (1984). Detachment ≠ “Meaning Detachment”. Journal of Semantics 3 (3):257-260.
Richard Brooks, The Cultivation of Cosmopolitan Detachment in Comparative Law: The Hellenistic Contributions.
Wieslaw Dziobiak (1977). On Detachment-Substitutional Formalization in Normal Modal Logics. Studia Logica 36 (3):165 - 171.
Michael Beeson, Robert Veroff & Larry Wos (2005). Double-Negation Elimination in Some Propositional Logics. Studia Logica 80 (2-3):195 - 234.
J. Roger Hindley (1993). BCK and BCI Logics, Condensed Detachment and the $2$-Property. [REVIEW] Notre Dame Journal of Formal Logic 34 (2):231-250.
J. Roger Hindley & David Meredith (1990). Principal Type-Schemes and Condensed Detachment. Journal of Symbolic Logic 55 (1):90-105.
Branden Fitelson, Vanquishing the XCB Question: The Methodological Discovery of the Last Shortest Single Axiom for the Equivalential Calculus.
M. W. Bunder (1995). A Simplified Form of Condensed Detachment. Journal of Logic, Language and Information 4 (2):169-173.
J. A. Kalman (1982). The Two-Property and Condensed Detachment. Studia Logica 41 (2-3):173 - 179.
Added to index2009-01-28
Total downloads11 ( #128,401 of 1,096,270 )
Recent downloads (6 months)1 ( #224,942 of 1,096,270 )
How can I increase my downloads?