|Abstract||Axiom 1 of K is the same as Axiom 1 in L, thus we have nothing to prove. Axiom 2 of K is 2(φ → ψ) → (2φ → 2ψ). We give a derivation of this formula in L: (φ → ψ) ∧ φ → ψ 2((φ → ψ) ∧ φ) → 2ψ (the rule from L) 2(φ → ψ) ∧ 2φ → 2ψ (axiom 3 of L and propositional logic) 2(φ → ψ) → (2φ → 2ψ) (propositional logic) Remain the rules of K. Modus ponens is a rule of both so there is nothing to prove. We show that L proves the Necessitation rule. That is, we have to show that if L φ, then L 2φ. The following derivation in L from assumption φ shows this: φ → φ (propositional logic) 2 → 2φ (the rule from L) 2φ (modus ponens using axiom 2 ) This completes the direction of the proof form left to right.|
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
|Through your library||Only published papers are available at libraries|
Similar books and articles
Bernard Walliser & Denis Zwirn (2002). Can Bayes' Rule Be Justified by Cognitive Rationality Principles? Theory and Decision 53 (2):95-135.
Dan E. Willard (2005). An Exploration of the Partial Respects in Which an Axiom System Recognizing Solely Addition as a Total Function Can Verify its Own Consistency. Journal of Symbolic Logic 70 (4):1171-1209.
Sachio Hirokawa (1996). The Proofs of Α→Α in P - W. Journal of Symbolic Logic 61 (1):195-211.
Robert E. Beaudoin (1987). Strong Analogues of Martin's Axiom Imply Axiom R. Journal of Symbolic Logic 52 (1):216-218.
T. Thacher Robinson (1968). Independence of Two Nice Sets of Axioms for the Propositional Calculus. Journal of Symbolic Logic 33 (2):265-270.
Robert Goldblatt (1982). The Semantics of HOARE's Iteration Rule. Studia Logica 41 (2-3):141 - 158.
A. Avron (1998). Multiplicative Conjunction and an Algebraic Meaning of Contraction and Weakening. Journal of Symbolic Logic 63 (3):831-859.
Michael Beeson, Robert Veroff & Larry Wos (2005). Double-Negation Elimination in Some Propositional Logics. Studia Logica 80 (2-3):195 - 234.
Renate A. Schmidt & Dmitry Tishkovsky (2008). On Combinations of Propositional Dynamic Logic and Doxastic Modal Logics. Journal of Logic, Language and Information 17 (1):109-129.
Added to index2010-04-09
Total downloads16 ( #81,690 of 722,750 )
Recent downloads (6 months)2 ( #36,437 of 722,750 )
How can I increase my downloads?