ترغب بنشر مسار تعليمي؟ اضغط هنا

An extension of Krachts theorem to generalized Sahlqvist formulas

119   0   0.0 ( 0 )
 نشر من قبل Stanislav Kikot
 تاريخ النشر 2010
  مجال البحث
والبحث باللغة English
 تأليف Stanislav Kikot




اسأل ChatGPT حول البحث

Sahlqvist formulas are a syntactically specified class of modal formulas proposed by Hendrik Sahlqvist in 1975. They are important because of their first-order definability and canonicity, and hence axiomatize complete modal logics. The first-order properties definable by Sahlqvist formulas were syntactically characterized by Marcus Kracht in 1993. The present paper extends Krachts theorem to the class of `generalized Sahlqvist formulas introduced by Goranko and Vakarelov and describes an appropriate generalization of Kracht formulas.

قيم البحث

اقرأ أيضاً

Generalized polynomials are mappings obtained from the conventional polynomials by the use of operations of addition, multiplication and taking the integer part. Extending the classical theorem of H. Weyl on equidistribution of polynomials, we show t hat a generalized polynomial $q(n)$ has the property that the sequence $(q(n) lambda)_{n in mathbb{Z}}$ is well distributed $bmod , 1$ for all but countably many $lambda in mathbb{R}$ if and only if $limlimits_{substack{|n| rightarrow infty n otin J}} |q(n)| = infty$ for some (possibly empty) set $J$ having zero density in $mathbb{Z}$. We also prove a version of this theorem along the primes (which may be viewed as an extension of classical results of I. Vinogradov and G. Rhin). Finally, we utilize these results to obtain new examples of sets of recurrence and van der Corput sets.
We show that Morleys theorem on the number of countable models of a countable first-order theory becomes an undecidable statement when extended to second-order logic. More generally, we calculate the number of equivalence classes of $sigma$-projectiv e equivalence relations in several models of set theory. Our methods include random and Cohen forcing, Woodin cardinals and Inner Model Theory.
In this paper, we will give an extension of Moks theorem on the generalized Frankel conjecture under the condition of the orthogonal bisectional curvature.
A classical theorem of Herglotz states that a function $nmapsto r(n)$ from $mathbb Z$ into $mathbb C^{stimes s}$ is positive definite if and only there exists a $mathbb C^{stimes s}$-valued positive measure $dmu$ on $[0,2pi]$ such that $r(n)=int_0^{2 pi}e^{int}dmu(t)$for $nin mathbb Z$. We prove a quaternionic analogue of this result when the function is allowed to have a number of negative squares. A key tool in the argument is the theory of slice hyperholomorphic functions, and the representation of such functions which have a positive real part in the unit ball of the quaternions. We study in great detail the case of positive definite functions.
The commutative ambiguity of a context-free grammar G assigns to each Parikh vector v the number of distinct leftmost derivations yielding a word with Parikh vector v. Based on the results on the generalization of Newtons method to omega-continuous s emirings, we show how to approximate the commutative ambiguity by means of rational formal power series, and give a lower bound on the convergence speed of these approximations. From the latter result we deduce that the commutative ambiguity itself is rational modulo the generalized idempotence identity k=k+1 (for k some positive integer), and, subsequently, that it can be represented as a weighted sum of linear sets. This extends Parikhs well-known result that the commutative image of context-free languages is semilinear (k=1). Based on the well-known relationship between context-free grammars and algebraic systems over semirings, our results extend the work by Green et al. on the computation of the provenance of Datalog queries over commutative omega-continuous semirings.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا