a basis for a mathematical theory of computation
... of information. The present paper contains no information about this. The present paper is divided into two sections. The first contains several descriptive formalisms with a few examples of their use, and the second contains what little theory we have that enables us to prove the equivalence of com ...
... of information. The present paper contains no information about this. The present paper is divided into two sections. The first contains several descriptive formalisms with a few examples of their use, and the second contains what little theory we have that enables us to prove the equivalence of com ...
CS2300-1.7
... • In math, CS, and other disciplines, informal proofs which are generally shorter, are generally used. ...
... • In math, CS, and other disciplines, informal proofs which are generally shorter, are generally used. ...
Godel`s Proof
... of axioms and a fixed set of typographical rules, one could shunt symbols around and produce new strings of symbols, called “theorems.” The pinnacle of this movement was a monumental three-volume work by Bertrand Russell and Alfred North Whitehead called Principia Mathematica, which came out in the y ...
... of axioms and a fixed set of typographical rules, one could shunt symbols around and produce new strings of symbols, called “theorems.” The pinnacle of this movement was a monumental three-volume work by Bertrand Russell and Alfred North Whitehead called Principia Mathematica, which came out in the y ...
Everything is Knowable - Computer Science Intranet
... 3. Successful – the Dynamic Turn The further development of the Moore-sentence firstly gives a multi-agent perspective of announcements of the form “(I tell you that:) p is true and you don’t know that”, and, secondly, gives a dynamic perspective namely that such announcements cannot be believed aft ...
... 3. Successful – the Dynamic Turn The further development of the Moore-sentence firstly gives a multi-agent perspective of announcements of the form “(I tell you that:) p is true and you don’t know that”, and, secondly, gives a dynamic perspective namely that such announcements cannot be believed aft ...
Mathematical Induction
... An alternative approach, taken in Fitch, is to treat < as a legitimate symbol of the language, defined by the (additional Peano) axiom xy[x
... An alternative approach, taken in Fitch, is to treat < as a legitimate symbol of the language, defined by the (additional Peano) axiom xy[x
An Automata Theoretic Decision Procedure for the Propositional Mu
... Propositional versions of the mu-calculus have been proposed by Pratt (1981) and Kozen (1982). These logics use a least lixpoint construct to increase the expressive power of propositional dynamic logic (PDL) of Fischer and Ladner (1979). Kozen’s formulation captures the infinite looping construct o ...
... Propositional versions of the mu-calculus have been proposed by Pratt (1981) and Kozen (1982). These logics use a least lixpoint construct to increase the expressive power of propositional dynamic logic (PDL) of Fischer and Ladner (1979). Kozen’s formulation captures the infinite looping construct o ...
Robust Satisfaction - CS
... Two possible views regarding the nature of time induce two types of temporal logics [Lam80]. In linear temporal logics, time is treated as if each moment in time has a unique possible future. Thus, linear temporal logic formulas are interpreted over linear sequences and we regard them as describing ...
... Two possible views regarding the nature of time induce two types of temporal logics [Lam80]. In linear temporal logics, time is treated as if each moment in time has a unique possible future. Thus, linear temporal logic formulas are interpreted over linear sequences and we regard them as describing ...
Section 3.6: Indirect Argument: Contradiction and Contraposition
... So far, we have only considered so called “direct proofs” of mathematical statements. Specifically, we have been given a statement to prove, and then we have used the definitions and previous results to logically derive the statement. In this section we consider “indirect proofs” proofs which do not ...
... So far, we have only considered so called “direct proofs” of mathematical statements. Specifically, we have been given a statement to prove, and then we have used the definitions and previous results to logically derive the statement. In this section we consider “indirect proofs” proofs which do not ...
Philosophy of Logic and Language
... Second, then, proponents of the proof-theoretic approach can say that a conclusion φ is a logical consequence of a set of premises Γ IFF there is a proof of φ from the members of Γ in some system (of a certain sort) or other. ...
... Second, then, proponents of the proof-theoretic approach can say that a conclusion φ is a logical consequence of a set of premises Γ IFF there is a proof of φ from the members of Γ in some system (of a certain sort) or other. ...
On Countable Chains Having Decidable Monadic Theory.
... one of M . In this paper we prove that this property holds for every infinite countable chain, namely that no infinite countable chain is maximal with respect to MSO logic. The proof relies on the composition method developed by Feferman–Vaught [9], Läuchli [15] and Shelah [20], which reduces the MSO ...
... one of M . In this paper we prove that this property holds for every infinite countable chain, namely that no infinite countable chain is maximal with respect to MSO logic. The proof relies on the composition method developed by Feferman–Vaught [9], Läuchli [15] and Shelah [20], which reduces the MSO ...
Gentzen`s original consistency proof and the Bar Theorem
... plays no role in the proof of consistency: that proof is obtained by means of the notion of a reduction procedure for deductions of sequents in the formal system of first-order number theory in natural deduction and an assignment of ordinals to these deductions such that each reduction step results ...
... plays no role in the proof of consistency: that proof is obtained by means of the notion of a reduction procedure for deductions of sequents in the formal system of first-order number theory in natural deduction and an assignment of ordinals to these deductions such that each reduction step results ...
Least and greatest fixed points in Ludics, CSL 2015, Berlin.
... qa = Ω otherwise. We denote by Ω− the design a(~xa ) binds the variables ~xa appearing in pa . Variables which are not under the scope of a binder are free. The free variables of a design d are denoted by fv(d). We identify two designs which are α-equivalent, i.e., which are equal up to renaming of ...
... qa = Ω otherwise. We denote by Ω− the design a(~xa ) binds the variables ~xa appearing in pa . Variables which are not under the scope of a binder are free. The free variables of a design d are denoted by fv(d). We identify two designs which are α-equivalent, i.e., which are equal up to renaming of ...
A Survey on Small Fragments of First-Order Logic over Finite
... between automata and logic goes back to Büchi. He used monadic second-order logic (MSO) for describing properties of words. Hence, every sentence in MSO defines a language by specifying the set of all words having this property. He gave effective transformations of MSO sentences into finite automat ...
... between automata and logic goes back to Büchi. He used monadic second-order logic (MSO) for describing properties of words. Hence, every sentence in MSO defines a language by specifying the set of all words having this property. He gave effective transformations of MSO sentences into finite automat ...
On the computational content of intuitionistic propositional proofs
... logic. This property of the intuitionistic calculus has been extensively studied, but mostly from the point of view of computability and little has been proved about computational complexity. The aim of this paper is to show that the constructive character of intuitionistic logic manifests itself no ...
... logic. This property of the intuitionistic calculus has been extensively studied, but mostly from the point of view of computability and little has been proved about computational complexity. The aim of this paper is to show that the constructive character of intuitionistic logic manifests itself no ...
LOGIC I 1. The Completeness Theorem 1.1. On consequences and
... model of T . Does the converse hold? The question was posed in the 1920’s by David Hilbert (of the 23 problems fame). The answer is that remarkably, yes, it does! This result, known as the Completeness Theorem for first-order logic, was proved by Kurt Gödel in 1929. According to the Completeness Th ...
... model of T . Does the converse hold? The question was posed in the 1920’s by David Hilbert (of the 23 problems fame). The answer is that remarkably, yes, it does! This result, known as the Completeness Theorem for first-order logic, was proved by Kurt Gödel in 1929. According to the Completeness Th ...
