PRESERVATION OF ADMISSIBLE RULES WHEN COMBINING LOGICS

2016 ◽  
Vol 9 (4) ◽  
pp. 641-663 ◽  
Author(s):  
JOÃO RASGA ◽  
CRISTINA SERNADAS ◽  
AMÍLCAR SERNADAS
Keyword(s):  
Wide Class ◽  
Time Complexity ◽  
Weak Form ◽  
Modal Logics ◽  
Mild Conditions ◽  
Admissible Rules ◽  
Structural Completeness ◽  
Combining Logics

AbstractAdmissible rules are shown to be conservatively preserved by the meet-combination of a wide class of logics. A basis is obtained for the resulting logic from bases given for the component logics, under mild conditions. A weak form of structural completeness is proved to be preserved by the combination. Decidability of the set of admissible rules is also shown to be preserved, with no penalty on the time complexity. Examples are provided for the meet-combination of intermediate and modal logics.

ON THE AVERAGE CASE CIRCUIT DELAY OF DISJUNCTION

1995 ◽  
Vol 05 (02) ◽  
pp. 275-280 ◽  
Author(s):  
BEATE BOLLIG ◽  
MARTIN HÜHNE ◽  
STEFAN PÖLT ◽  
PETR SAVICKÝ
Keyword(s):  
Lower Bounds ◽  
Wide Class ◽  
Time Complexity ◽  
Upper And Lower Bounds ◽  
Average Case ◽  
Asymptotically Optimal ◽  
Circuit Delay ◽  
Suitable Measure

For circuits the expected delay is a suitable measure for the average case time complexity. In this paper, new upper and lower bounds on the expected delay of circuits for disjunction and conjunction are derived. The circuits presented yield asymptotically optimal expected delay for a wide class of distributions on the inputs even when the parameters of the distribution are not known in advance.

scholarly journals Fusions of Description Logics and Abstract Description Systems

2002 ◽  
Vol 16 ◽  
pp. 1-58 ◽  
Author(s):  
F. Baader ◽  
C. Lutz ◽  
H. Sturm ◽  
F. Wolter
Keyword(s):  
Large Class ◽  
Description Logics ◽  
General Setting ◽  
Modal Logics ◽  
Common Generalization ◽  
Abstract Description ◽  
Normal Modal Logics ◽  
Combining Logics

Fusions are a simple way of combining logics. For normal modal logics, fusions have been investigated in detail. In particular, it is known that, under certain conditions, decidability transfers from the component logics to their fusion. Though description logics are closely related to modal logics, they are not necessarily normal. In addition, ABox reasoning in description logics is not covered by the results from modal logics. In this paper, we extend the decidability transfer results from normal modal logics to a large class of description logics. To cover different description logics in a uniform way, we introduce abstract description systems, which can be seen as a common generalization of description and modal logics, and show the transfer results in this general setting.

Hereditarily structurally complete modal logics

1995 ◽  
Vol 60 (1) ◽  
pp. 266-288 ◽  
Author(s):  
V. V. Rybakov
Keyword(s):  
Modal Logic ◽  
Modal Logics ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Structural Completeness ◽  
Necessary And Sufficient

AbstractWe consider structural completeness in modal logics. The main result is the necessary and sufficient condition for modal logics over K4 to be hereditarily structurally complete: a modal logic λ is hereditarily structurally complete iff λ is not included in any logic from the list of twenty special tabular logics. Hence there are exactly twenty maximal structurally incomplete modal logics above K4 and they are all tabular.

scholarly journals UNIVERSALITY OF ZETA-FUNCTIONS OF CUSP FORMS AND NON-TRIVIAL ZEROS OF THE RIEMANN ZETA-FUNCTION

2021 ◽  
Vol 26 (1) ◽  
pp. 82-93
Author(s):  
Aidas Balčiūnas ◽  
Violeta Franckevič ◽  
Virginija Garbaliauskienė ◽  
Renata Macaitienė ◽  
Audronė Rimkevičienė
Keyword(s):  
Zeta Function ◽  
Wide Class ◽  
Riemann Zeta Function ◽  
Analytic Functions ◽  
Pair Correlation ◽  
Zeta Functions ◽  
Weak Form ◽  
Cusp Forms ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

It is known that zeta-functions ζ(s,F) of normalized Hecke-eigen cusp forms F are universal in the Voronin sense, i.e., their shifts ζ(s + iτ,F), τ R, approximate a wide class of analytic functions. In the paper, under a weak form of the Montgomery pair correlation conjecture, it is proved that the shifts ζ(s+iγkh,F), where γ1 < γ2 < ... is a sequence of imaginary parts of non-trivial zeros of the Riemann zeta function and h > 0, also approximate a wide class of analytic functions.

scholarly journals Admissible Rules of Modal Logics

2005 ◽  
Vol 15 (4) ◽  
pp. 411-431 ◽  
Author(s):  
Emil Jeřábek
Keyword(s):  
Modal Logics ◽  
Admissible Rules

Bases of admissible rules in modal logics S4.2 and S4.2Grz

1993 ◽  
Vol 32 (2) ◽  
pp. 63-70
Author(s):  
S. V. Babenyshev
Keyword(s):  
Modal Logics ◽  
Admissible Rules

scholarly journals An Extension of Geiringer's Theorem for a Wide Class of Evolutionary Search Algorithms

2006 ◽  
Vol 14 (1) ◽  
pp. 87-118 ◽  
Author(s):  
Boris Mitavskiy ◽  
Jonathan Rowe
Keyword(s):  
Evolutionary Algorithm ◽  
Wide Class ◽  
Transition Matrix ◽  
General Theorem ◽  
Search Space ◽  
Evolutionary Search ◽  
Mild Conditions ◽  
Markov Transition Matrix ◽  
Markov Transition ◽  
The Family

The frequency with which various elements of the search space of a given evolutionary algorithm are sampled is affected by the family of recombination (reproduction) operators. The original Geiringer theorem tells us the limiting frequency of occurrence of a given individual under repeated application of crossover alone for the classical genetic algorithm. Recently, Geiringer's theorem has been generalized to include the case of linear GP with homologous crossover (which can also be thought of as a variable length GA). In the current paper we prove a general theorem which tells us that under rather mild conditions on a given evolutionary algorithm, call it A, the stationary distribution of a certain Markov chain of populations in the absence of selection is unique and uniform. This theorem not only implies the already existing versions of Geiringer's theorem, but also provides a recipe of how to obtain similar facts for a rather wide class of evolutionary algorithms. The techniques which are used to prove this theorem involve a classical fact about random walks on a group and may allow us to compute and/or estimate the eigenvalues of the corresponding Markov transition matrix which is directly related to the rate of convergence towards the unique limiting distribution.

UNIFICATION IN SUPERINTUITIONISTIC PREDICATE LOGICS AND ITS APPLICATIONS

2018 ◽  
Vol 12 (1) ◽  
pp. 37-61 ◽  
Author(s):  
WOJCIECH DZIK ◽  
PIOTR WOJTYLAK
Keyword(s):  
Propositional Logic ◽  
Predicate Logic ◽  
Order Logic ◽  
Existential Quantifier ◽  
First Order ◽  
Admissible Rules ◽  
Structural Completeness ◽  
Individual Variables ◽  
Definition Of ◽  
Finitely Presented

AbstractWe introduce unification in first-order logic. In propositional logic, unification was introduced by S. Ghilardi, see Ghilardi (1997, 1999, 2000). He successfully applied it in solving systematically the problem of admissibility of inference rules in intuitionistic and transitive modal propositional logics. Here we focus on superintuitionistic predicate logics and apply unification to some old and new problems: definability of disjunction and existential quantifier, disjunction and existential quantifier under implication, admissible rules, a basis for the passive rules, (almost) structural completeness, etc. For this aim we apply modified specific notions, introduced in propositional logic by Ghilardi, such as projective formulas, projective unifiers, etc.Unification in predicate logic seems to be harder than in the propositional case. Any definition of the key concept of substitution for predicate variables must take care of individual variables. We allow adding new free individual variables by substitutions (contrary to Pogorzelski & Prucnal (1975)). Moreover, since predicate logic is not as close to algebra as propositional logic, direct application of useful algebraic notions of finitely presented algebras, projective algebras, etc., is not possible.

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