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1.
S. K. Thomason 《Studia Logica》1980,39(2-3):143-144
We show that the join of two classical [respectively, regular, normal] modal logics employing distinct modal operators is a conservative extension of each of them.This work was supported by the National Research Council of Canada and by the Polish Academy of Sciences. 相似文献
2.
Martin Amerbauer 《Studia Logica》1996,57(2-3):359-372
We give sound and complete tableau and sequent calculi for the prepositional normal modal logics S4.04, K4B and G
0(these logics are the smallest normal modal logics containing K and the schemata A A, A A and A ( A); A A and AA; A A and ((A A) A) A resp.) with the following properties: the calculi for S4.04 and G
0are cut-free and have the interpolation property, the calculus for K4B contains a restricted version of the cut-rule, the so-called analytical cut-rule.In addition we show that G
0is not compact (and therefore not canonical), and we proof with the tableau-method that G
0is characterised by the class of all finite, (transitive) trees of degenerate or simple clusters of worlds; therefore G
0is decidable and also characterised by the class of all frames for G
0.Research supported by Fonds zur Förderung der wissenschaftlichen Forschung, project number P8495-PHY.Presented by W. Rautenberg 相似文献
3.
Rajeev Goré 《Studia Logica》1994,53(3):433-457
We present sound, (weakly) complete and cut-free tableau systems for the propositional normal modal logicsS4.3, S4.3.1 andS4.14. When the modality is given a temporal interpretation, these logics respectively model time as a linear dense sequence of points; as a linear discrete sequence of points; and as a branching tree where each branch is a linear discrete sequence of points.Although cut-free, the last two systems do not possess the subformula property. But for any given finite set of formulaeX the superformulae involved are always bounded by a finite set of formulaeX*
L depending only onX and the logicL. Thus each system gives a nondeterministic decision procedure for the logic in question. The completeness proofs yield deterministic decision procedures for each logic because each proof is constructive.Each tableau system has a cut-free sequent analogue proving that Gentzen's cut-elimination theorem holds for these latter systems. The techniques are due to Hintikka and Rautenberg.Presented byDov M. Gabbay 相似文献
4.
5.
Michael J. White 《Studia Logica》1981,40(1):75-87
This paper specifies classes of framesmaximally omnitemporally characteristic for Thomas' normal modal logicT
2
+
and for each logic in the ascending chain of Segerberg logics investigated by Segerberg and Hughes and Cresswell. It is shown that distinct a,scending chains of generalized Segerberg logics can be constructed from eachT
n
+
logic (n 2). The set containing allT
n
+
and Segerberg logics can be totally- (linearly-) ordered but not well-ordered by the inclusion relation. The order type of this ordered set is
*( + 1). Throughout the paper my approach is fundamentally semantical.I should like to thank Professor G. E. Hughes for helpful comments on an earlier draft of this paper. 相似文献
6.
《Journal of Applied Logic》2014,12(3):349-368
This paper examines two aspects of propositional probabilistic logics: the nesting of probabilistic operators, and the expressivity of probabilistic assessments. We show that nesting can be eliminated when the semantics is based on a single probability measure over valuations; we then introduce a classification for probabilistic assessments, and present novel results on their expressivity. Logics in the literature are categorized using our results on nesting and on probabilistic expressivity. 相似文献
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9.
Ramon Jansana 《Studia Logica》1995,55(2):273-299
In this paper we develop a general framework to deal with abstract logics associated with a given modal logic. In particular we study the abstract logics associated with the weak and strong deductive systems of the normal modal logicK and its intuitionistic version. We also study the abstract logics that satisfy the conditionC
+(X)=C(
in
I
n
X) and find the modal deductive systems whose abstract logics, in addition to being classical or intuitionistic, satisfy that condition. Finally we study the deductive systems whose abstract logics satisfy, in addition to the already mentioned properties, the property that the operatorC
+ is classical relative to some new defined operations.Work partially supported by Spanish DGICYT grant PB90-0465-C02-01.Presented byJan Zygmunt 相似文献
10.
11.
This paper is a survey of results concerning embeddings of intuitionistic propositional logic and its extensions into various classical modal systems. 相似文献
12.
Minghui Ma 《Frontiers of Philosophy in China》2010,5(2):294-311
Adding certain cardinality quantifiers into first-order language will give substantially more expressive languages. Thus,
many mathematical concepts beyond first-order logic can be handled. Since basic modal logic can be seen as the bisimular invariant
fragment of first-order logic on the level of models, it has no ability to handle modally these mathematical concepts beyond
first-order logic. By adding modalities regarding the cardinalities of successor states, we can, in principle, investigate
modal logics of all cardinalities. Thus ways of exploring model-theoretic logics can be transferred to modal logics. 相似文献
13.
Slavian Radev 《Studia Logica》1987,46(4):291-309
A logic with normal modal operators and countable infinite conjunctions and disjunctions is introduced. A Hilbert's style axiomatization is proved complete for this logic, as well as for countable sublogics and subtheories. It is also shown that the logic has the interpolation property. 相似文献
14.
This paper is a survey of results concerning the disjunction property, Halldén-completeness, and other related properties of intermediate prepositional logics and normal modal logics containing S4. 相似文献
15.
Silvio Ghilardi 《Studia Logica》1992,51(2):195-214
The quantified extension of a canonical prepositional intermediate logic is complete with respect to the generalization of Kripke semantics taking into consideration set-valued functors defined on a category. 相似文献
16.
André Fuhrmann 《Studia Logica》1990,49(4):501-514
Semantics are given for modal extensions of relevant logics based on the kind of frames introduced in [7]. By means of a simple recipe we may obtain from a class FRM (L) of unreduced frames characterising a (non-modal) logic L, frame-classes FRM
(L.M) characterising conjunctively regular modal extensions L.M of L. By displaying an incompleteness phenomenon, it is shown how the recipe fails when reduced frames are under consideration. 相似文献
17.
Resolution-based methods for modal logics 总被引:2,自引:0,他引:2
18.
Wieslaw Dziobiak 《Studia Logica》1977,36(3):165-171
The aim of this paper is to propose a criterion of finite detachment-substitutional formalization for normal modal systems. The criterion will comprise only those normal modal systems which are finitely axiomatizable by means of the substitution, detachment for material implication and Gödel rules.Some results of this paper were announced in the abstract [2].Allatum est die 10 Junii 1976 相似文献
19.
Larisa Maksimova 《Studia Logica》1991,50(3-4):457-471
This is a survey of results on interpolation in propositional normal modal logics. Interpolation properties of these logics are closely connected with amalgamation properties of varieties of modal algebras. Therefore, the results on interpolation are also reformulated in terms of amalgamation. 相似文献
20.
Kripke-style models with two accessibility relations, one intuitionistic and the other modal, are given for analogues of the
modal systemK based on Heyting's prepositional logic. It is shown that these two relations can combine with each other in various ways.
Soundness and completeness are proved for systems with only the necessity operator, or only the possibility operator, or both.
Embeddings in modal systems with several modal operators, based on classical propositional logic, are also considered. This
paper lays the ground for an investigation of intuitionistic analogues of systems stronger thanK. A brief survey is given of the existing literature on intuitionistic modal logic. 相似文献