H. Sahlqvist. Completeness and correspondence in the rst and second order semantics for modal logic. In S. Kanger, ed., Proceedings of the 3d Scandinavian Logic Symposium, pp. 110-143. North-Holland, 1975.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of a regular grammar logic with converse. One can add a set of converses to the alphabet and extend the frame into a h [ i frame) 3. Originally, grammar logics are de ned with formal grammars in [FdCP88] as in [Bal98,Dem01,Dem02] and they form a subclass of Sahlqvist modal logics [Sah75] with frame conditions expressible in 1 when S is context free. In the present paper, we adopt a lighter presentation with the introduction of semi Thue systems that are more appropriate. Example 1. The standard modal logics K, T, B, S4, K5, K45, and S5 can be de ned as regular grammar logics ....

H. Sahlqvist. Completeness and correspondence in the rst and second order semantics for modal logics. In S. Kanger, editor, 3rd Scandinavian Logic Symposium, Uppsala, Sweden, 1973, pages 110-143. North Holland, 1975.

....the usual test axiom with: p ]q ( p q) In accordance with this axiom, the formula [p ]q can be read as q is known with respect to p being known . Thus, we think of the modal operator [ as the operator of relative knowledge. Using the elimination of second order quanti ers [4, 7] it is easy to nd the corresponding semantic de nition for the new operator. Thus, a (PDL S5) model is a tuple hS; Q; R; j=i satisfying all the properties of PDL S5 model, except the meaning of is speci ed by: Q( f(s; t) 2 R j t j= g: This induces the notions of [PDL; ....

H. Sahlqvist. Completeness and correspondence in the rst and second order semantics for modal logics. In S. Kanger, editor, Proc. 3rd Scandinavian Logic Symposium, 1973.

....to formal grammars. Namely, with each production rule i 1 : i n j 1 : j n in the grammar is associated a modal axiom [i 1 ] i n ]p ) j 1 ] j n 0 ]p. Such axioms are called reduction principles in [Ben76, CS94] and they are a special type of Sahlqvist formulae [Sah75] and primitive formulae [Kra96] They are typical in modal logic. In this paper, we study the extensions of the multimodal logic Km with m independent K modal connectives by nite addition of axiom schemes of the above form such that the associated nite set of production rules forms a regular ....

....validity and frame conditions. Theorem 6 Let G be a formal grammar. For u; v 2 (N[ I) u ) G v i (II) u]p ) v]p is L m valid i (III) for all L m models R v R u . The equivalence between (II) and (III) is a classical correspondence result in modal logic theory (see e.g. [Sah75, Ben84]) I) implies (II) can be proved by induction on the length of the derivation. II) implies (I) can be shown by easily adapting the proof of [Bal98, Theorem IV.2.1] Actually, II) implies (I) can be also proved without any reference to tableaux calculi. Indeed, the proof of [CS94, Theorem 3] ....

H. Sahlqvist. Completeness and correspondence in the rst and second order semantics for modal logics. In S. Kanger, editor, 50 3rd Scandinavian Logic Symposium, Uppsala, Sweden, 1973, pages 110-143. North Holland, 1975.

....u 2 U 8x x 2 u ) f(x) 2 w which is implied by (6) choose u = w) Thus, 8x x f(x) in the Boolean algebra implies 8U U f 00 (U) in its set representation. So called preservation theorems give syntactic characterizations of properties which transfer to the full powerset al..gebra (see Sahlqvist [19] and J onsson [8] Quanti er elimination comes into the play if we want to express the given property of f 00 in terms of the accessibility relation R introduced above. For example 8U U f 00 (U) can be written as 8U 8w w 2 U ) 9u R(w; u) u 2 U . Since 8U quanti es over the whole powerset ....

....above. 6 Observe that the positive and negative occurrences of P are not separated, thus Lemma 2.1 cannot be applied ELIMINATION OF PREDICATE QUANTIFIERS 179 6. 2 The Sahlqvist van Benthem Algorithm The Sahlqvist van Benthem algorithm was motivated by the modal correspondence theory (see [19, 23]) It is based on the idea of nding minimal substitutions for the eliminated predicates. The key role is played here by second order Sahlqvist formulae that re ect a particular class of modal axioms (for a general de nition see de Rijke [18] The Sahlqvist van Benthem algorithm is based on ....

Henrik Sahlqvist. Completeness and correspondence in the rst and second-order semantics for modal logic. In S. Kanger, editor, Proc. 3rd Scandinavian Logic Symposium, North Holland, 110-143, 1975.

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Sahlqvist, H., Completeness and correspondence in the rst and second order semantics for modal logic, Proceedings of the Third Scandinavian Logic Symposium (Univ. Uppsala, Uppsala,

No context found.

H. Sahlqvist. Completeness and correspondence in the rst and second order semantics for modal logic. In S. Kanger, ed., Proceedings of the 3d Scandinavian Logic Symposium, pp. 110-143. North-Holland, 1975.

No context found.

H. Sahlqvist. Completeness and correspondence in the rst and second order semantics for modal logics. In S. Kanger, editor, 3rd Scandinavian Logic Symposium, Uppsala, Sweden,

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