Results 1  10
of
1,073,922
Secondorder logic and foundations of mathematics
 The Bulletin of Symbolic Logic
, 2001
"... We discuss the differences between firstorder set theory and secondorder logic as a foundation for mathematics. We analyse these languages in terms of two levels of formalization. The analysis shows that if secondorder logic is understood in its full semantics capable of characterizing categorical ..."
Abstract

Cited by 29 (3 self)
 Add to MetaCart
We discuss the differences between firstorder set theory and secondorder logic as a foundation for mathematics. We analyse these languages in terms of two levels of formalization. The analysis shows that if secondorder logic is understood in its full semantics capable of characterizing
Asymptotic Monadic SecondOrder Logic
"... Abstract. In this paper we introduce socalled asymptotic logics, logics that are meant to reason about weights of elements in a model in a way inspired by topology. Our main subject of study is Asymptotic Monadic SecondOrder Logic over infinite words. This is a logic talking about ωwords labelled ..."
Abstract
 Add to MetaCart
Abstract. In this paper we introduce socalled asymptotic logics, logics that are meant to reason about weights of elements in a model in a way inspired by topology. Our main subject of study is Asymptotic Monadic SecondOrder Logic over infinite words. This is a logic talking about ω
SecondOrder Logic, a Language Theoretic Approach
, 2011
"... Graph structure and monadic secondorder logic. A languagetheoretic approach. ..."
Abstract
 Add to MetaCart
Graph structure and monadic secondorder logic. A languagetheoretic approach.
Quantitative monadic secondorder logic
 In Proceedings of LICS’13
, 2013
"... Abstract—While monadic secondorder logic is a prominent logic for specifying languages of finite words, it lacks the power to compute quantitative properties, e.g. to count. An automata model capable of computing such properties are weighted automata, but logics equivalent to these automata have o ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract—While monadic secondorder logic is a prominent logic for specifying languages of finite words, it lacks the power to compute quantitative properties, e.g. to count. An automata model capable of computing such properties are weighted automata, but logics equivalent to these automata have
Approximation and Existential SecondOrder Logic
, 1990
"... The approximation properties of NPcomplete optimization problems vary considerably. While for some problems, the solution cannot be approximated with constant accuracy unless P=NP, others can be approximated to any arbitrary degree of accuracy. In between there are problems for which approximat ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
expressive power of existential secondorder logic; it contains the classes MAX SNP, MAX NP [PY88], and MAX \Pi 1 [PR90] as lowest classes. 1 Introduction Approximate solutions for NPhard optimization problems are important in practice and appealing in the theory of algorithms and complexity
SECOND ORDER LOGIC OR SET THEORY?
"... Abstract. We try to answer the question which is the “right ” foundation of mathematics, second order logic or set theory. Since the former is usually thought of as a formal language and the latter as a first order theory, we have to rephrase the question. We formulate what we call the second order ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Abstract. We try to answer the question which is the “right ” foundation of mathematics, second order logic or set theory. Since the former is usually thought of as a formal language and the latter as a first order theory, we have to rephrase the question. We formulate what we call the second order
Arity and Alternation in Second Order Logic
, 1996
"... . We investigate the expressive power of second order logic over finite structures, when two limitations are imposed. Let SAA(k;n) (AA(k;n)) be the set of second order formulas such that the arity of the relation variables is bounded by k and the number of alternations of (both first order and) sec ..."
Abstract
 Add to MetaCart
. We investigate the expressive power of second order logic over finite structures, when two limitations are imposed. Let SAA(k;n) (AA(k;n)) be the set of second order formulas such that the arity of the relation variables is bounded by k and the number of alternations of (both first order and
MONA: Monadic SecondOrder Logic in Practice
 IN PRACTICE, IN TOOLS AND ALGORITHMS FOR THE CONSTRUCTION AND ANALYSIS OF SYSTEMS, FIRST INTERNATIONAL WORKSHOP, TACAS '95, LNCS 1019
, 1995
"... The purpose of this article is to introduce Monadic Secondorder Logic as a practical means of specifying regularity. The logic is a highly succinct alternative to the use of regular expressions. We have built a tool MONA, which acts as a decision procedure and as a translator to finitestate au ..."
Abstract

Cited by 148 (20 self)
 Add to MetaCart
The purpose of this article is to introduce Monadic Secondorder Logic as a practical means of specifying regularity. The logic is a highly succinct alternative to the use of regular expressions. We have built a tool MONA, which acts as a decision procedure and as a translator to finite
On Spatial Conjunction as SecondOrder Logic
, 2004
"... Spatial conjunction is a powerful construct for reasoning about dynamically allocated data structures, as well as concurrent, distributed and mobile computation. While researchers have identified many uses of spatial conjunction, its precise expressive power compared to traditional logical constr ..."
Abstract

Cited by 9 (1 self)
 Add to MetaCart
Spatial conjunction is a powerful construct for reasoning about dynamically allocated data structures, as well as concurrent, distributed and mobile computation. While researchers have identified many uses of spatial conjunction, its precise expressive power compared to traditional logical
Results 1  10
of
1,073,922