Graduate studies at Western
Erkenntnis 43 (1):81 - 109 (1995)
|Abstract||We construct an extension P of the standard language of classical propositional logic by adjoining to the alphabet of a new category of logical-pragmatic signs. The well formed formulas of are calledradical formulas (rfs) of P;rfs preceded by theassertion sign constituteelementary assertive formulas of P, which can be connected together by means of thepragmatic connectives N, K, A, C, E, so as to obtain the set of all theassertive formulas (afs). Everyrf of P is endowed with atruth value defined classically, and everyaf is endowed with ajustification value, defined in terms of the intuitive notion of proof and depending on the truth values of its radical subformulas. In this framework, we define the notion ofpragmatic validity in P and yield a list of criteria of pragmatic validity which hold under the assumption that only classical metalinguistic procedures of proof be accepted. We translate the classical propositional calculus (CPC) and the intuitionistic propositional calculus (IPC) into the assertive part of P and show that this translation allows us to interpret Intuitionistic Logic as an axiomatic theory of the constructive proof concept rather than an alternative to Classical Logic. Finally, we show that our framework provides a suitable background for discussing classical problems in the philosophy of logic.|
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
Peter Roeper & Hugues Leblanc (1999). Absolute Probability Functions for Intuitionistic Propositional Logic. Journal of Philosophical Logic 28 (3):223-234.
Tomasz Połacik (1994). Second Order Propositional Operators Over Cantor Space. Studia Logica 53 (1):93 - 105.
Philip Kremer (1997). On the Complexity of Propositional Quantification in Intuitionistic Logic. Journal of Symbolic Logic 62 (2):529-544.
Tomasz Połacik (1998). Propositional Quantification in the Monadic Fragment of Intuitionistic Logic. Journal of Symbolic Logic 63 (1):269-300.
Morten H. Sørensen & Paweł Urzyczyn (2010). A Syntactic Embedding of Predicate Logic Into Second-Order Propositional Logic. Notre Dame Journal of Formal Logic 51 (4):457-473.
A. S. Troelstra (1981). On a Second Order Propositional Operator in Intuitionistic Logic. Studia Logica 40 (2):113 - 139.
David Ellerman (2010). The Logic of Partitions: Introduction to the Dual of the Logic of Subsets. Review of Symbolic Logic 3 (2):287-350.
A. D. Yashin (1999). Irreflexive Modality in the Intuitionistic Propositional Logic and Novikov Completeness. Journal of Philosophical Logic 28 (2):175-197.
Peter W. O'Hearn & David J. Pym (1999). The Logic of Bunched Implications. Bulletin of Symbolic Logic 5 (2):215-244.
Andrew M. Pitts (1992). On an Interpretation of Second Order Quantification in First Order Intuitionistic Propositional Logic. Journal of Symbolic Logic 57 (1):33-52.
Added to index2009-01-28
Total downloads12 ( #101,269 of 739,375 )
Recent downloads (6 months)1 ( #61,680 of 739,375 )
How can I increase my downloads?