L. Maksimova. Amalgamation and interpolation in normal modal logics. Studia Logica, L(3/4):457--471, 1991. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Constructive Interpolation in Hybrid Logic - Blackburn, Marx (2002) (Correct)
.... S4, and S5) interpolation goes through smoothly (see for example Fitting [7] or Rautenberg [12] But even in the propositional case, once one leaves these simple logics, interpolation results are hard to come by (it fails, for example, in the modal logic of Church Rosser frames, and see Maksimova [10] for results above S4) And in the first order case, positive interpolation results are few and far between (Fine [6] showed that none of the first order constant domain modal logics between K and S5 has interpolation) Failure of interpolation (and in particular of the closely associated Beth ....
L. Maksimova. Amalgamation and interpolation in normal modal logics. Studia Logica, L(3/4):457--471, 1991.
Interpolation and Bisimulation in Temporal Logic - Areces, de Rijke (1998) (3 citations) (Correct)
....hold. Conversely, disproving SIP (or TIP) implies the failure of all of them. In the rest of the article j= refers always to the global consequence relation. 3 Interpolation in Classical Modal Logic Important general results concerning interpolation for standard modal logics are known, witness [13]. These results are a byproduct of the strong connections between the interpolation property and the algebraic property of amalgamation. In this paper we will discuss two recent results providing, respectively, a method to prove AIP and a method to disprove SIP. First, the following notions should ....
L. Maksimova. Amalgamation and interpolation in normal modal logics. Studia Logica, L(3/4):457--471, 1991.
Lazy-formalization to the Frame Problem - Foo (2002) (1 citation) (Correct)
....to take advantage of its sound and complete axiomatization and well developed Kripkean semantics. Although the interpolation property of dynamic logic is an open problem 2 , the interpolation property of normal modal logics has been intensively investigated in recent years with positive results([Maksimova 1991;Madarasz 1995;Marx 1999] 2 Reasoning with action description in PDL Reasoning about action is one of the motivations the dynamic logic was proposed (see the preface of [Harel 1979] In dynamic logic, effects of actions are expressed by modal formulas. A represents always causes A , ....
L. Maksimova, Amalgamation and interpolation in normal modal logics, Studia Logica, L(3/4), 457-471, 1991.
Interpolation in Algebraizable Logics; Semantics for.. - Madarász (1998) (1 citation) (Correct)
....for Non normal Multi modal Logic Judit X. Madar asz Mathematical Institute, Budapest, P.O.Box 127 H 1364 Hungary. e mail: madarasz math inst.hu ABSTRACT. The two main directions pursued in the present paper are the following. The first direction was (perhaps) started by Pigozzi in 1969. In [Mak 91] and [Mak 79] Maksimova proved that a normal modal logic (with a single unary modality) has the Craig interpolation property iff the corresponding class of algebras has the superamalgamation property. In this paper we extend Maksimova s theorem to normal multi modal logics with arbitrarily many, ....
....of algebras has property alg(P ) where alg(P ) is a natural algebraic property. More on this subject can be found, e.g. in the Introduction of Andr eka et al. AKNS 94] and in BlokPigozzi [BP 89] BP] In Sections 4 6 we prove (or state) equivalence theorems of the above kind. Namely, in [Mak 91] and [Mak 79] Maksimova proved that a normal modal logic (with one unary modality) has the Craig interpolation property iff the corresponding class of algebras has the superamalgamation property. These notions will be recalled below. One of the first results of this type (involving Craig ....
L. L. Maksimova, Amalgamation and interpolation in normal modal logics, Studia Logica, L(3/4), (1991), pp. 457--471.
Hybrid Logics: Characterization, Interpolation and Complexity - Areces, Blackburn, Marx (Correct)
....be any frame condition in the bounded fragment. The theory in the hybrid language H(#; of the class frames(8 x: x) enjoys strong interpolation (AIP) This result stands in sharp contrast to the scarcity of general interpolation results obtained for the basic modal language; see for example [Mak91] Indeed, it can be viewed as delineating the syntactic form of interpolants in modal logic as follows. Let L be the modal logic in the basic modal language of a rst order de nable class frames of frames. Now, even if we cannot nd interpolants in the modal language itself, we can always nd ....
L. Maksimova. Amalgamation and interpolation in normal modal logics. Studia Logica, L(3/4):457-471, 1991.
Modal Logic and non-well-founded Set Theory: translation.. - D'Agostino (1998) (Correct)
....Z i is a bisimulation between M and N . Amalgamation. Amalgamation is a classical tool which is often used to prove interpolation. There is a long tradition in the area of algebraic logic connecting (algebraic) amalgamation properties with (logical) interpolation properties (e.g. 1] 55] [49], and [50] In this dissertation we shall use a construction (related to the zig zag products of [50] that amalgamates two structures, which are bisimilar with respect to the common language, in a third one. 2.2.10. Lemma. Let M, N be structures for the languages L and L 0 respectively. If M ....
L. Maksimova. Amalgamation and interpolation in normal modal logics. Studia Logica, L(3/4):457-471, 1991.
Relativized Relation Algebras - Marx (1999) (2 citations) (Correct)
....Theorem 2.2. Remarks 4.4 Amalgamation is interesting for a number of reasons, one is its connection with interpolation (cf. for instance (Pigozzi, 1972; Andr eka et al. 1994b) The classes in Theorem 4. 2 enjoy even a stronger form of amalgamation super amalgamation, a concept originating with (Maksimova, 1991). This can be shown by the same construction as used above to show SAP, cf (Marx, 1995) Madar asz, 1998b) proved for a broad class of logics that arrow interpolation (whenever j= there exists an interpolant such that j= and j= is equivalent with super amalgamation. This ....
Maksimova, L. (1991). Amalgamation and interpolation in normal modal logics. Studia Logica, L(3/4):457--471.
Constructive Interpolation in Hybrid Logic - Blackburn, Marx (2002) (Correct)
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L. Maksimova. Amalgamation and interpolation in normal modal logics. Studia Logica, L(3/4):457--471, 1991.
Interpolation in Modal Logic - Maarten Marx Institute (1999) (2 citations) (Correct)
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Maksimova, L. (1991). Amalgamation and interpolation in normal modal logics. Studia Logica, L(3/4):457--471.
Interpolation Properties of Action Logic: Lazy-formalization to .. - Zhang, Foo (Correct)
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L. Maksimova, Amalgamation and interpolation in normal modal logics, Studia Logica, L(3/4), 457-471, 1991.
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