Modal logics with two kinds of necessity and possibility.
Paul A. Weingartner · Notre Dame Journal of Formal Logic · 1968
Structure of the system.1.08 Definition of the system SSI.1.10-1.26Matrices of the operations 1.4 Truth in SSI and SS1M.1.5 Characteristical value (cv) of a formula.1.6 Concept of logical consequence in SSI and SS1M.1.7 Consistency of SSI and SS1M.1.8 Decision procedure for SSI and SS1M.1.9 (Modal) variations of formulas in SSI and SS1M. 2. Basic laws (theorems) of SSI and SS1M.2.1 Identity and Negation.2.2 Conjunction.2.3 Disjunction.2.4 Implication and Equivalence.3. Investigations on the validity of axiom systems of propositional calculus in SSI and SS1M.3.0 Classical propositional calculus.This paper was read at the Colloquium on Logic and Foundations of Mathematics at Hannover, Germany, from August 8 to 12, 1966 organized by the Deutsche Vereinigung fur Mathematische Logik und fur Grundlagenforschung der exakten Wissenschaften, held as the 1966 European meeting of the Association of Symbolic Logic.The results of the 2., 3. and 5. chapter of this paper have been computed to a great deal with the help of the electronic computer of the Philosophical Faculty of the University of Innsbruck (chairman: Prof.