|Appears in Collections:||Law and Philosophy Journal Articles|
|Peer Review Status:||Refereed|
|Title:||A refinement of the Craig–Lyndon Interpolation Theorem for classical first-order logic with identity (Forthcoming/Available Online)|
|Keywords:||Craig–Lyndon Interpolation Theorem (for classical first-order logic)|
Kleene’s strong 3-valued logic
Priest’s Logic of Paradox
Belnap’s four-valued logic
|Citation:||Milne P A refinement of the Craig–Lyndon Interpolation Theorem for classical first-order logic with identity (Forthcoming/Available Online), Logique et Analyse.|
|Abstract:||We refine the interpolation property of classical first-order logic (without identity and without functionsymbols), showing that if G & , & D and G $ D then there is an interpolant c, constructed using onlynon-logical vocabulary common to both members of G and members of D, such that (i) G entails c in thefirst-order version of Kleene's strong three-valued logic, and (ii) c entails D in the first-order version ofPriest's Logic of Paradox. The proof proceeds via a careful analysis of derivations employing semantictableaux. Lyndon's strengthening of the interpolation property falls out of an observation regardingsuch derivations and the steps involved in the construction of interpolants.Through an analysis of tableaux rules for identity, the proof is then extended to classical first-orderlogic with identity (but without function symbols).|
|Rights:||Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work. Proper attribution of authorship and correct citation details should be given. Authors are permitted to post the published version of the work in an institutional repository and on a personal website, with an acknowledgement of its initial publication in this journal.|
|first-order interpolation LetA FINAL corrected.pdf||254.61 kB||Adobe PDF||View/Open|
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