H. J. Ohlbach and R. A. Schmidt. Functional translation and second-order frame properties of modal logics. J. Logic Computat., 7(5):581--603, 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....alternative translation mappings from modal logics into subclasses of first order logic which satisfy the mentioned minimal requirements. These include the functional translation (Auffray and Enjalbert, 1992; Fari nas del Cerro and Herzig, 1988; Ohlbach, 1991) the optimised functional translation (Ohlbach and Schmidt, 1997; Schmidt, 1997) and the semi functional translation (Nonnengart, 1995) The advantages of the translation approach include the following. First, by enabling the use of a variety of first order and propositional theorem provers the translation approach provides access to efficient, reliable and ....

H. J. Ohlbach and R. A. Schmidt. Functional translation and second-order frame properties of modal logics. Journal of Logic and Computation, 7(5):581--603, 1997.

.... be embedded into a decidable fragment of predicate logic [AvBN98] Hence, there are two general approaches for reasoning with KR : dedicated decision procedures [Lad77, SSS91, GS96] and the translation into first order logic followed by the application of an existing first order theorem prover [OS97, Sch97]. To compete with the dedicated algorithms, the second approach has to yield a decision procedure and it has This papers appeared in the Journal of Logic and Computation, Vol. 10 No. 99 47, pp. 1 22 2000. 1 to be efficient, because the dedicated algorithms usually have optimal worst case ....

H. J. Ohlbach and R. A. Schmidt. Functional translation and second-order frame properties of modal logics. Journal of Logic and Computation, 7(5):581--603, October 1997.

.... can be embedded into a decidable fragment of predicate logic [AvBN98] Hence, there are two general approaches for reasoning with KR : dedicated decision procedures [Lad77, SSS91, GS96] and the translation into rst order logic followed by the application of an existing rst order theorem prover [OS97, Sch97]. To compete with the dedicated algorithms, the second approach has to yield a decision procedure and it has to be ecient, because the dedicated algorithms usually have optimal worst case complexity. For KR , the rst issue is solved and, regarding the complexity, experimental results show that ....

H. J. Ohlbach and R. A. Schmidt. Functional translation and secondorder frame properties of modal logics. Journal of Logic and Computation, 7(5):581-603, October 1997.

.... can be embedded into a decidable fragment of predicate logic [AvBN98] Hence, there are two general approaches for reasoning with KR : dedicated decision procedures [Lad77,SSS91,GS96] and the translation into first order logic followed by the application of an existing first order theorem prover [OS97,Sch97]. To compete with the dedicated algorithms, the second approach has to yield a decision procedure and it has to be efficient, because the dedicated algorithms usually have optimal worst case complexity. For KR , the first issue is solved and, regarding the complexity, experimental results show ....

H. J. Ohlbach and R. A. Schmidt. Functional translation and secondorder frame properties of modal logics. Journal of Logic and Computation, 7(5):581--603, October 1997.

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H. J. Ohlbach and R. A. Schmidt. Functional translation and second-order frame properties of modal logics. J. Logic Computat., 7(5):581--603, 1997.

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H. J. Ohlbach and R. A. Schmidt. Functional translation and second-order frame properties of modal logics. Tech. Rep. MPI-I-952 -002, MPI Informatik, Saarbrucken, January 1995.

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H. J. Ohlbach and R. A. Schmidt. Functional translation and second-order frame properties of modal logics. Journal of Logic and Computation, 7(5):581--603, 1997.

No context found.

H. J. Ohlbach and R. A. Schmidt. Functional translation and second-order frame properties of modal logics. Journal of Logic and Computation, 7(5):581--603, October 1997.

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H. J. Ohlbach and R. A. Schmidt. Functional translation and second-order frame properties of modal logics. J. Logic Computat., 7(5):581-603, 1997.

....include the following. Non standard translation approaches. Non standard translation methods include reductions derived from the functional semantics of normal modal logics with unparameterised modalities, namely the functional translation [1, 35, 59] the optimised functional translation [35, 63, 76] and the semi functional translation [56] Surveys of the di#erent translation methods of modal logics and other non classical logics are [60, 61, 62] These non standard translation approaches are all implemented in mspass [46] Experience shows that the performance of first order theorem provers ....

H. J. Ohlbach and R. A. Schmidt. Functional translation and second-order frame properties of modal logics. Journal of Logic and Computation, 7(5):581--603, 1997.

....of the functional translation mapping which reduces local satisfiability in the modal logics K and KD to first order satisfiability. Thus, many of the properties of K and KD carry over to the functional modal fragment, among others also the permutability of universal and existential quantification [23] which reduces the functional modal fragment into the Bernays Schonfinkel class (the # prefix class) 14, 4] Permutability of universal and existential quantification is not generally applicable. For instance, it does not extend to full fluted logic; actually it does not even extend to the ....

H. J. Ohlbach and R. A. Schmidt. Functional translation and secondorder frame properties of modal logics. J. Logic Computat., 7(5):581-- 603, 1997.

....can be embedded in uted logic. Interestingly, translations of propositional modal formulae by both the relational translation and a variation of the functional translation (described and used in [11, 14] are uted formulae. This raises the question whether the results of Ohlbach and Schmidt [19, 26] can be generalised to uted logic. The answer to this question is negative, though. Already the use of the quanti er exchange operator, which swaps existential and universal quanti ers in a non standard fashion [19] leads to loss of soundness. A counter example is the relational translation of ....

....formulae. This raises the question whether the results of Ohlbach and Schmidt [19, 26] can be generalised to uted logic. The answer to this question is negative, though. Already the use of the quanti er exchange operator, which swaps existential and universal quanti ers in a non standard fashion [19], leads to loss of soundness. A counter example is the relational translation of the second formula in the class of branching K formulae, de ned in [10, Prop. 6.5] Historically, uted logic arose as a byproduct of the predicate functor logic introduced by Quine [25] Adding various combinatory ....

H. J. Ohlbach and R. A. Schmidt. Functional translation and second-order frame properties of modal logics. J. Logic Computat., 7(5):581-603, 1997.

....is lost during transformation to clausal form and subsequent deduction. By using a di erent translation method, for Resolution for Testing Modal Satis ability and Building Models 3 example, translation methods based on the functional translation where accessibility is encoded in terms of paths [2, 19, 36], this problem can be reduced and eliminated for certain logics [9, 12] There is another well known technique, called structural transformation or renaming, which enables the preservation of the structure of the original formula in the clausal form. This technique is used in connection with most ....

Ohlbach, H. J. and R. A. Schmidt: 1997, `Functional Translation and SecondOrder Frame Properties of Modal Logics'. Journal of Logic and Computation 7(5), 581-603. 34 Ullrich Hustadt and Renate A. Schmidt

....into clausal form, and (iii) saturation based resolution. In the current implementation of mspass the available translation methods include: the standard relational translation method, the functional translation method [1, 5, 14] the optimised functional translation method [15] including a variation de ned in terms of n ary predicates [7] as well as the semi functional translation method [12] The implementation of the relational translation method is most general and applies to the language described in Section 1. Some restrictions apply to the other methods. ....

H. J. Ohlbach and R. A. Schmidt. Functional translation and second-order frame properties of modal logics. J. Logic Computat., 7(5):581-603, 1997.

....A number of different translation methods are available in mspass. These include: ffl the standard relational translation method (which is determined by the usual semantics of the language) ffl the functional translation method [ 1; 4; 13 ] and ffl the optimised functional translation method [ 14 ] including a variation defined in terms of n ary predicates instead of unary predicates and paths [ 6; 7 ] as well as ffl the semi functional translation method [ 10; 11 ] In the current implementation the standard relational translation method is most general and applies to the language ....

H. J. Ohlbach and R. A. Schmidt. Functional translation and second-order frame properties of modal logics. J. Logic Computat., 7(5):581--603, 1997.

.... approaches for the basic propositional multi modal logic K(m) and its syntactical variant, the knowledge representation formalism ALC [19] Some approaches utilize standard first order theorem proving techniques in combination with translations from propositional modal logic to first order logic [13, 14, 15]. Others use Gentzen systems [10, 11] Still others use tableaux proof methods [7, 17, 1] Usually, the literature on theorem provers for modal logic confines itself to a description of the underlying calculus and methodology accompanied with a consideration of the worst case complexity of the ....

....The translation approach (TA) is based on the idea that modal inference can be done by translating modal formulae into first order logic and conventional first order theorem proving. The translation approach we use is the optimized functional translation approach described in Ohlbach and Schmidt [15]. It 14 has the property that ordinary resolution without any refinement strategies is a decision procedure for K(m) 18] The translation maps modal formulae into a logic, called basic path logic, which is a monadic fragment of sorted first order logic with one binary function symbol ffi that ....

Hans Jurgen Ohlbach and Renate A. Schmidt. Functional translation and second-order frame properties of modal logics. Research Report MPI-I-95-2-002, Max-Planck-Institut fur Informatik, Saarbrucken, Germany, January 1995.

....in Proc. of Intern. Workshop on Description Logics 99. Linkoping University. ffl the standard relational translation method (which is determined by the usual semantics of the language) ffl the functional translation method [ 1; 4; 13 ] and ffl the optimised functional translation method [ 14 ] including a variation defined in terms of n ary predicates instead of unary predicates and paths [ 6; 7 ] as well as ffl the semi functional translation method [ 10; 11 ] In the current implementation the standard relational translation method is most general and applies to the language ....

H. J. Ohlbach and R. A. Schmidt. Functional translation and second-order frame properties of modal logics. J. Logic Computat., 7(5):581--603, 1997.

....resembles branch pruning in the Logics Workbench) it has an extensive set of reduction rules including tautology deletion, subsumption and condensing, and it supports dynamic sort theories by additional inference and reduction rules. The translation we use is the optimised functional translation [2]. It maps normal propositional modal logics into a class of path logics. Path logics are clausal logics over the language of the monadic fragment of sorted first order logic with a special binary function symbol for defining accessibility. Clauses of path logics are restricted in that only Skolem ....

....are refinements of the general translation approach towards e#cient modal theorem proving. The optimised functional translation is applicable to many propositional modal logics, including K, KT, and S4 and their multi modal versions, but notably also to some second order modal logics, like KM [2]. A general result shows that any first order resolution theorem prover (with condensing) provides a decision procedure for a variety of modal logics [3] Hardware: Sun Ultra 1 Model 170E (167 MHz UltraSPARC processor, 512 KB second level cache) 192 MB main memory. Results: On classes of ....

H. J. Ohlbach and R. A. Schmidt. Functional translation and second-order frame properties of modal logics. Res. Report MPI-I-95-2-002, MPI f. Informatik, Saarbrucken, 1995.

....embed quantified modal logics into fragments of first order logic and employ first order resolution theorem proving. Zamov (1989) describes a lock decision procedure for the translation of S4. All procedures involve theory unification. The optimised functional translation method (Herzig 1989, Ohlbach and Schmidt 1997) applies to propositional normal modal logics and gives rise to a class of path logics, which this paper considers. Very much like modal logics, path logics form a lattice with the weakest being the basic path logic associated with the basic modal logic K and also KD. Different path logics are ....

Ohlbach, H. J. and Schmidt, R. A. (1997), Functional translation and second-order frame properties of modal logics, Journal of Logic and Computation 7(5), 581-- 603.

....multi modal logic KE . Unfortunately, one of the axioms, namely N7, is not first order definable in the standard Kripke semantics. Its relational translation N7 0 is a second order formula. So, instead of using the standard relational translation we use the functional translation as proposed in Ohlbach and Schmidt (1995) for non first order axioms like McKinsey s axiom. The functional translation method was proposed by various authors, for example Ohlbach (1988, 1991) Fari nas del Cerro and Herzig (1988) Herzig (1989) Auffray and Enjalbert (1992) and Zamov (1989) It exploits the fact that every binary ....

....together with the completeness of the transition from the relational to the functional representation (which is easy) guarantees completeness. If the second order formulae are not equivalent to first order formulae then completeness is still an open problem. Unfortunately this is the case for KE . Ohlbach and Schmidt (1995) prove the following relativized soundness and completeness result for the functional translation Pi f . Theorem 4.2 (Relative soundness and completeness of the functional translation) Let Phi be additional Hilbert axioms in a propositional modal logic K (m) and any modal formula. If the ....

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Ohlbach, H. J. and Schmidt, R. A. (1995), Functional translation and second-order frame properties of modal logics, Technical Report MPI-I-95-2-002, Max-PlanckInstitut fur Informatik, Saarbrucken, Germany. Submitted for publication in the Journal of Logic and Computation.

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