Results in Non-classical Propositional Logic |
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Page 8
... L that is closed under modus ponens ; however , in Chapter III we only require closure under a certain weakened form ... inconsistent iff , for all A , A is derivable from Σ in L ; if at least some A is not so derivable , Σ is L ...
... L that is closed under modus ponens ; however , in Chapter III we only require closure under a certain weakened form ... inconsistent iff , for all A , A is derivable from Σ in L ; if at least some A is not so derivable , Σ is L ...
Page 11
... L - inconsistent if A Σ . The canonical model ( for L ) is the model M1 = < XL , RL , PL ) , where X1 = { x : x≤ • & x is L - maximal } ; R1 = { ( x , y ) : x , yeX , & VA ( AЄx ⇒ AЄy ) } ; 91 ( Px ) = { x : x € X1 & P1 Ex } , for all k≥ ...
... L - inconsistent if A Σ . The canonical model ( for L ) is the model M1 = < XL , RL , PL ) , where X1 = { x : x≤ • & x is L - maximal } ; R1 = { ( x , y ) : x , yeX , & VA ( AЄx ⇒ AЄy ) } ; 91 ( Px ) = { x : x € X1 & P1 Ex } , for all k≥ ...
Common terms and phrases
accessibility relation author's axiomatization binary relation Boolean canonical model Chapter class of frames classical modal logic closed under subformulas complete with respect completeness results constants of degree contains Dana Scott defined by S4 denote derivable determined dissertation domain of F Dummett & Lemmon elements fails finite model property finitely axiomatizable fixed objects following schemata formula is valid frames iff Hence Hintikka intuitionistic logic Kanger Kripke L-consistent LEMMA Lemmata 1.1 Lemmon & Scott logical constants McKinsey frames McKinsey model McKinsey property modus ponens mula normal logic defined partially ordered frame Prior's proof propositional letters propositional logic pseudo-epimorphism reflexive and transitive relation of F S-cluster schema schemata S₁ Semantical analysis set of formulas set of propositional set the domain symmetric Tarski THEOREM 4.4 Theoria three-valued modal logic tions transitive McKinsey true valuation in F X₁ ZMLGM Α Ε Σ ΑΕΣ ΒΕΣ