Dynamic logic by David Harel, Dexter Kozen, Jerzy Tiuryn

By David Harel, Dexter Kozen, Jerzy Tiuryn

Among the ways to formal reasoning approximately courses, Dynamic common sense enjoys the singular good thing about being strongly with regards to classical common sense. Its variations represent typical generalizations and extensions of classical formalisms. for instance, Propositional Dynamic common sense (PDL) should be defined as a mix of 3 complementary classical parts: propositional calculus, modal common sense, and the algebra of normal occasions. In First-Order Dynamic common sense (DL), the propositional calculus is changed via classical first-order predicate calculus. Dynamic common sense is a procedure of exceptional team spirit that's theoretically wealthy in addition to of useful price. it may be used for formalizing correctness standards and proving carefully that these requirements are met through a specific application. different makes use of comprise selecting the equivalence of courses, evaluating the expressive strength of varied programming constructs, and synthesizing courses from requirements. This e-book offers the 1st entire advent to Dynamic good judgment. it truly is divided into 3 components. the 1st half reports the right basic strategies of common sense and computability idea and will stand by myself as an creation to those issues. the second one half discusses PDL and its versions, and the 3rd half discusses DL and its editions. Examples are supplied all through, and workouts and a brief historic part are integrated on the finish of every bankruptcy.

Show description

Read or Download Dynamic logic PDF

Similar logic books

Lectures on Algebraic Model Theory

Lately, version idea has had striking good fortune in fixing very important difficulties in addition to in laying off new gentle on our figuring out of them. the 3 lectures accumulated right here current fresh advancements in 3 such parts: Anand Pillay on differential fields, Patrick Speissegger on o-minimality and Matthias Clasen and Matthew Valeriote on tame congruence thought.

Foundations of Computing

Offers an creation to the speculation of computing technological know-how. masking the most components of complexity thought, automata and formal languages in a coherent means, the textual content additionally covers the theoretical points of extra utilized components. The author's process is to stimulate scholars' realizing of the relevance of conception to special software components - for instance, picture processing, verbal exchange networks and cryptography are all mentioned.

Compressed Data Structures for Strings: On Searching and Extracting Strings from Compressed Textual Data

Info compression is crucial to regulate substantial datasets, indexing is prime to question them. besides the fact that, their pursuits look as counterposed: the previous goals at minimizing facts redundancies, while the latter augments the dataset with auxiliary details to hurry up the question answer. during this monograph we introduce strategies that triumph over this dichotomy.

A Boole Anthology: Recent and Classical Studies in the Logic of George Boole

Sleek mathematical good judgment wouldn't exist with out the analytical instruments first built by way of George Boole within the Mathematical research of common sense and The legislation of suggestion. The impression of the Boolean university at the improvement of common sense, continually regarded yet lengthy underestimated, has lately develop into an incredible examine subject.

Extra resources for Dynamic logic

Sample text

V 1 v 1, and def ` v `0 () 8c `(c) v `0 (c) and ^, _, and : are computed on f0 ? 1g according to the following tables: _: 0 ? 1 :: 1 0 0 0 ? 1 0 1 ? ? 1 ? ? 1 1 1 1 1 1 0 In other words, ^ gives the greatest lower bound and _ gives the least upper bound ^: 0 ? 1 0 0 0 0 ? 0 ? MIT Press Math7X9/2000/06/30:10:36 Page 37 Computability and Complexity 37 in the order 0 ? 1, and : inverts the order. The labeling ` can be computed as the v-least xpoint of the monotone map : flabelingsg ! flabelingsg, where 8 > > > > < def (`)(c) = > > > > : V 1 f`(d) j c ;!

We culminate with a general theorem due to Knaster and Tarski concerning inductive de nitions. Let U be a xed set. Recall that 2U denotes the powerset of U , or the set of MIT Press Math7X9/2000/06/30:10:36 Page 17 Mathematical Preliminaries 17 subsets of U : 2U def = fA j A U g: A set operator on U is a function : 2U ! 2U . Monotone, Continuous, and Finitary Operators A set operator is said to be monotone if it preserves set inclusion: B =) A (A) (B ): A chain of sets in U is a family of subsets of U totally ordered by the inclusion relation that is, for every A and B in the chain, either A B or B A.

If is an ordinal, then so is f g. The latter is called S the successor of and is denoted + 1. Also, if A is any set of ordinals, then A is an ordinal and is the MIT Press Math7X9/2000/06/30:10:36 Page 15 Mathematical Preliminaries 15 supremum of the ordinals in A under the relation . The smallest few ordinals are 0 def = ? g 2 def = f0 1g = f? gg def 3 = f0 1 2g = f? g f? ggg .. The rst in nite ordinal is ! def = f0 1 2 3 : : : g: An ordinal is called a successor ordinal if it is of the form +1 for some ordinal , otherwise it is called a limit ordinal .

Download PDF sample

Rated 4.10 of 5 – based on 7 votes