Bolesław Sobociński. Remarks about axiomatizations of certain modal systems. Notre Dame journal of formal logic, vol. 5 no. 1 (1964), pp. 71–80. - A. N. Prior, K1, K2 and related modal systems. Notre Dame journal of formal logic, vol. 5 no. 4 (for 1964, pub. 1965), pp. 299–304. - Bolesław Sobociński. Modal system S4.4. Notre Dame journal of formal logic, vol. 5 no. 4 (for 1964, pub. 1965), pp. 305–312. - Bolesław Sobociński. Family of the non-Lewis modal systems. Notre Dame journal of formal logic, vol. 5 no. 4 (for 1964, pub. 1965), pp. 313–318. - Ivo Thomas. A theorem on S4.2 and S4.4. Notre Dame journal of formal logic, vol. 8 no. 4 (for 1967, pub. 1968), pp. 335–336. - Ivo Thomas. Decision for K4. Notre Dame journal of formal logic, vol. 8 no. 4 (for 1967, pub. 1968), pp. 337–338.

1972 ◽  
Vol 37 (1) ◽  
pp. 182-183
Author(s):  
G. F. Schumm
Keyword(s):  
Formal Logic ◽  
Modal System ◽  
Modal Systems

New foundations for Lewis modal systems

1957 ◽  
Vol 22 (2) ◽  
pp. 176-186 ◽  
Author(s):  
E. J. Lemmon
Keyword(s):  
Modal Logic ◽  
Propositional Calculus ◽  
Modal System ◽  
New Foundations ◽  
Image Position ◽  
Classical Propositional Calculus ◽  
Modal Systems

The main aims of this paper are firstly to present new and simpler postulate sets for certain well-known systems of modal logic, and secondly, in the light of these results, to suggest some new or newly formulated calculi, capable of interpretation as systems of epistemic or deontic modalities. The symbolism throughout is that of [9] (see especially Part III, Chapter I). In what follows, by a Lewis modal system is meant a system which (i) contains the full classical propositional calculus, (ii) is contained in the Lewis system S5, (iii) admits of the substitutability of tautologous equivalents, (iv) possesses as theses the four formulae:We shall also say that a system Σ1 is stricter than a system Σ2, if both are Lewis modal systems and Σ1 is contained in Σ2 but Σ2 is not contained in Σ1; and we shall call Σ1absolutely strict, if it possesses an infinity of irreducible modalities. Thus, the five systems of Lewis in [5], S1, S2, S3, S4, and S5, are all Lewis modal systems by this definition; they are in an order of decreasing strictness from S1 to S5; and S1 and S2 alone are absolutely strict.

Results concerning same modal systems that contain S2

1964 ◽  
Vol 29 (2) ◽  
pp. 79-87 ◽  
Author(s):  
Lennart Åqvist
Keyword(s):  
Finite Number ◽  
Modal System ◽  
Modal Systems

It is well known that if a postulate LLCpp or a rule of procedure ├α→├Lα (from a thesis α of a considered system to infer a thesis Lα of that system) is added to Lewis's modal system S3, we get his system S4 (see [7], p. 148). It is also known that the addition of this rule to S2 and SI has the effect of converting these systems into the Gödel-Feys-von Wright system T (M). My purpose in this paper is first to draw attention to some other ways of converting S3 and S2 into S4 and T respectively, as well as to extend a theorem of Halldén on S3, S4 and S7 to S2, T and S6. The results reached will also apply to the systems S3.5, S5 and S7.5, where S3.5 and S7.5 are obtained, respectively, from S3 and S7 by the addition of the postulate CNLpLNLp; an answer will be given to the question of irreducible modalities in S3.5. Moreover, two results will be proved that bear on the problem whether the systems S2 and T can be axiomatized by means of a finite number of axiom schemata and material detachment as the only primitive rule of inference.

The expression of modality in Logoori

2020 ◽  
Vol 41 (2) ◽  
pp. 195-238
Author(s):  
John Gluckman ◽  
Margit Bowler
Keyword(s):  
Theoretical Analysis ◽  
Modal System ◽  
Linguistic Typology ◽  
Semantic Map ◽  
Link Type ◽  
Contemporary Research ◽  
New Approaches ◽  
Bantu Language ◽  
Phd Thesis ◽  
Modal Systems

Abstract This study presents a theoretically informed description of the expression of modality in Logoori (Luyia; Bantu). We document verbal and non-verbal modal expressions in Logoori, and show how these expressions fit into proposed typologies of modal systems (Kratzer, Angelika. 1981. The notional category of modality. In Hans-Jurgen Eikmeyer & Hannes Rieser (eds.), Words, worlds, and contexts: New approaches in word semantics, 38–74. Berlin: Mouton de Gruyter, Kratzer, Angelika. 1991. Modality. In Armin von Stechow & Dieter Wunderlich (eds.), Semantics: An international handbook of contemporary research, 639–650. Berlin: Mouton de Gruyter; van der Auwera, Johan & Vladimir Plungian. 1998. Modality’s semantic map. Linguistic Typology 2. 79–124. https://doi.org/10.1515/lity.1998.2.1.79; Nauze, Fabrice. 2008. Modality in typological perspective. Amsterdam: Institute for Logic, Language, and Computation PhD thesis). We show that Logoori’s modal system raises some interesting questions regarding the typology and theoretical analysis of modality and its relationship to other kinds of meaning. Our study contributes to the nascent but growing research on modal systems cross linguistically by adding data from an understudied Bantu language.

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