What is modal logic

http://lindquistlab.wi.mit.edu/PDFs/Alberti2009Cell.pdf

A systematic survey identifies prions and illuminates sequence features of prionogenic proteins

Definition des fragments modaux de la logique des predicats a partir de formules du premier ordre qui sont des traductions des proprietes poly-modales elementaires. Distinguant les fragments variables et finis des fragments lies a un quantificateur, l'A. developpe une version semantique des fragments gardes en remplacant les liens syntaxiques par des restrictions sur les types d'attribution dans les modeles generalises. Se referant a l'algebre cylindrique, l'A. indique les nouvelles directions que peuvent prendre les theoremes de Tarski dans un environnement mathematique: celle des contraintes structurelles speciales, des extensions infinies, de la logique modale etendue et d'une semantique dynamique

Modal languages and bounded fragments of predicate logic

Thank you for downloading classical descriptive set theory. Maybe you have knowledge that, people have search numerous times for their chosen novels like this classical descriptive set theory, but end up in infectious downloads. Rather than reading a good book with a cup of tea in the afternoon, instead they juggled with some malicious virus inside their laptop. classical descriptive set theory is available in our book collection an online access to it is set as public so you can download it instantly. Our digital library hosts in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the classical descriptive set theory is universally compatible with any devices to read.

Classical Descriptive Set Theory

Logic, Semantics, Metamathematics. By A. Tarski. Translated by J. H. Woodger. Pp. 471. 60s. 1956. (Clarendon Press)

Dependence is a common phenomenon, wherever one looks: ecological systems, astronomy, human history, stock markets - but what is the logic of dependence? This book is the first to carry out a systematic logical study of this important concept, giving on the way a precise mathematical treatment of Hintikka's independence friendly logic. Dependence logic adds the concept of dependence to first order logic. Here the syntax and semantics of dependence logic are studied, dependence logic is given an alternative game theoretic semantics, and results about its complexity are proven. This is a graduate textbook suitable for a special course in logic in mathematics, philosophy and computer science departments, and contains over 200 exercises, many of which have a full solution at the end of the book. It is also accessible to readers, with a basic knowledge of logic, interested in new phenomena in logic.

Dependence Logic: A New Approach to Independence Friendly Logic

We introduce an atomic formula $${\vec{y} \bot_{\vec{x}}\vec{z}}$$ intuitively saying that the variables $${\vec{y}}$$ are independent from the variables $${\vec{z}}$$ if the variables $${\vec{x}}$$ are kept constant. We contrast this with dependence logic $${\mathcal{D}}$$ based on the atomic formula = $${(\vec{x}, \vec{y})}$$ , actually equivalent to $${\vec{y} \bot_{\vec{x}}\vec{y}}$$ , saying that the variables $${\vec{y}}$$ are totally determined by the variables $${\vec{x}}$$ . We show that $${\vec{y} \bot_{\vec{x}}\vec{z}}$$ gives rise to a natural logic capable of formalizing basic intuitions about independence and dependence. We show that $${\vec{y} \bot_{\vec{x}}\vec{z}}$$ can be used to give partially ordered quantifiers and IF-logic an alternative interpretation without some of the shortcomings related to so called signaling that interpretations using = $${(\vec{x}, \vec{y})}$$ have.

/pdf/dependence-and-independence-4sroa27zd0.pdf

Dependence and Independence

We discuss the differences between first-order set theory and second-order logic as a foundation for mathematics. We analyse these languages in terms of two levels of formalization. The analysis shows that if second-order logic is understood in its full semantics capable of characterizing categorically central mathematical concepts, it relies entirely on informal reasoning. On the other hand, if it is given a weak semantics, it loses its power in expressing concepts categorically. First-order set theory and second-order logic are not radically different: the latter is a major fragment of the former.

/pdf/second-order-logic-and-foundations-of-mathematics-2b3doumysc.pdf

Second-Order Logic and Foundations of Mathematics

Generalized quantifiers and pebble games on finite structures

We study the expressive power of open formulas of dependence logic introduced in Vaananen [Dependence logic (Vol. 70 of London Mathematical Society Student Texts), 2007]. In particular, we answer a question raised by Wilfrid Hodges: how to characterize the sets of teams definable by means of identity only in dependence logic, or equivalently in independence friendly logic.

/pdf/on-definability-in-dependence-logic-9smrykklgz.pdf

Jouko Väänänen

Papers

Dependence Logic: A New Approach to Independence Friendly Logic

Dependence and Independence

Second-Order Logic and Foundations of Mathematics

Generalized quantifiers and pebble games on finite structures

On Definability in Dependence Logic