Die Grundlagen der Arithmetik §§82–83
... Frege observes that it has not yet been stated that every number immediately follows or is followed by another. He then states: 6. Every number except 0 immediately follows a number in the natural sequence of numbers. It is clear from §44 of Grundgesetze6 that Frege did not take (6) to imply that 0 ...
... Frege observes that it has not yet been stated that every number immediately follows or is followed by another. He then states: 6. Every number except 0 immediately follows a number in the natural sequence of numbers. It is clear from §44 of Grundgesetze6 that Frege did not take (6) to imply that 0 ...
An Institution-Independent Generalization of Tarski`s Elementary
... computer science. Besides their great generality, another important feature of institutions, not present, or poorly present, in other abstract frameworks, is the flexible support for language translations. This feature, particularly useful in formal specification and the semantics of programming lan ...
... computer science. Besides their great generality, another important feature of institutions, not present, or poorly present, in other abstract frameworks, is the flexible support for language translations. This feature, particularly useful in formal specification and the semantics of programming lan ...
Divide and congruence: From decomposition of modal formulas to preservation of branching and eta-bisimilarity
... algebra with a structural operational semantics in the De Simone format. To decide whether a process algebra term satisfies a modal formula, one can check whether its subterms satisfy certain other formulas, obtained by decomposing the original formula. This method was extended by Bloom, Fokkink & v ...
... algebra with a structural operational semantics in the De Simone format. To decide whether a process algebra term satisfies a modal formula, one can check whether its subterms satisfy certain other formulas, obtained by decomposing the original formula. This method was extended by Bloom, Fokkink & v ...
full text (.pdf)
... although with a little extra work this result can be shown to follow from a 1979 result of Berstel 2] (see also 9]). The proof in 17] only needed extra commutativity conditions of the form bp = pb, where b is a test. But as shown in that paper, this equation is equivalent to bpb + bpb = 0. Thus i ...
... although with a little extra work this result can be shown to follow from a 1979 result of Berstel 2] (see also 9]). The proof in 17] only needed extra commutativity conditions of the form bp = pb, where b is a test. But as shown in that paper, this equation is equivalent to bpb + bpb = 0. Thus i ...
Abella: A System for Reasoning about Relational Specifications
... font: in addition, keywords are depicted in blue. The types, terms, and formulas used by Abella are described briefly below as well as in the table in Figure 1. Types in Abella are the simple types; such types are either primitive types or built from two types using the arrow type constructor →. The ...
... font: in addition, keywords are depicted in blue. The types, terms, and formulas used by Abella are described briefly below as well as in the table in Figure 1. Types in Abella are the simple types; such types are either primitive types or built from two types using the arrow type constructor →. The ...
abdullah_thesis_slides.pdf
... are equal. It is denoted A ∼d,t B. Theorem Given d ∈ N and two structures A and B, if A ∼d B then there exists a fixed t∈ N such that A ∼d,t B. Theorem (Hanf’s theorem for EMSO) ...
... are equal. It is denoted A ∼d,t B. Theorem Given d ∈ N and two structures A and B, if A ∼d B then there exists a fixed t∈ N such that A ∼d,t B. Theorem (Hanf’s theorem for EMSO) ...
Chu Spaces - Stanford University
... It is convenient to view Chu spaces as organized either by rows or by columns. For the former, we define r̂ : A → (X → Σ) as r̂(a)(x) = r(a, x), and refer to the function r̂(a) : X → Σ as row a of A. Dually we define ř : X → (A → Σ) as ř(x)(a) = r(a, x) and call ř(x) : A → Σ column x of A. When r ...
... It is convenient to view Chu spaces as organized either by rows or by columns. For the former, we define r̂ : A → (X → Σ) as r̂(a)(x) = r(a, x), and refer to the function r̂(a) : X → Σ as row a of A. Dually we define ř : X → (A → Σ) as ř(x)(a) = r(a, x) and call ř(x) : A → Σ column x of A. When r ...
.pdf
... cost. Examples in the remainder of this section convey a sense for how an environment is represented by a TLA formula. ...
... cost. Examples in the remainder of this section convey a sense for how an environment is represented by a TLA formula. ...
lecture notes in logic - UCLA Department of Mathematics
... 4A. Tarski and Gödel (First Incompleteness Theorem). . . . . . . . . . . 139 4B. Numeralwise representability in Q . . . . . . . . . . . . . . . . . . . . . . . . . . 145 4C. Rosser, more Gödel and Löb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 4D. Computability and undec ...
... 4A. Tarski and Gödel (First Incompleteness Theorem). . . . . . . . . . . 139 4B. Numeralwise representability in Q . . . . . . . . . . . . . . . . . . . . . . . . . . 145 4C. Rosser, more Gödel and Löb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 4D. Computability and undec ...
The Lambda Calculus is Algebraic - Department of Mathematics and
... point of view. We suggest another way of looking at the problem, which yields a sense in which the lambda calculus is equivalent to an algebraic theory. The basic observation is that the failure of the ξ-rule is not a deficiency of the lambda calculus itself, nor of combinatory algebras, but rather ...
... point of view. We suggest another way of looking at the problem, which yields a sense in which the lambda calculus is equivalent to an algebraic theory. The basic observation is that the failure of the ξ-rule is not a deficiency of the lambda calculus itself, nor of combinatory algebras, but rather ...
MoL-2013-07 - Institute for Logic, Language and Computation
... the type of model-transformation technique that we are considering, they are not purely questions about these techniques. In this thesis, we are (for the most part) not interested in this interplay between a modeltransformation technique and sentences in the language of set theory, but instead, in ...
... the type of model-transformation technique that we are considering, they are not purely questions about these techniques. In this thesis, we are (for the most part) not interested in this interplay between a modeltransformation technique and sentences in the language of set theory, but instead, in ...
Mathematical Logic Prof. Arindama Singh Department of
... So, now if you look back, you can see that there are three proof procedures we have developed, calculations, informal proofs, and the resolutions. But all of them are semantic in nature. They first assume that there is some truth defined in it; because in calculations, you need equivalent substituti ...
... So, now if you look back, you can see that there are three proof procedures we have developed, calculations, informal proofs, and the resolutions. But all of them are semantic in nature. They first assume that there is some truth defined in it; because in calculations, you need equivalent substituti ...
A Unified View of Induction Reasoning for First-Order Logic
... strategy to perform lazy induction on particular explicit induction proofs. Kapur and Subramaniam [29] devised a method that extends schemata-based induction to deal with a special class of mutually defined functions. Courant [18] identified a class of implicit induction inference systems for which ...
... strategy to perform lazy induction on particular explicit induction proofs. Kapur and Subramaniam [29] devised a method that extends schemata-based induction to deal with a special class of mutually defined functions. Courant [18] identified a class of implicit induction inference systems for which ...
The Journal of Functional and Logic Programming The MIT Press
... ϑ a value assignment, or valuation, to a set of variables. As usual, the letter ω denotes the first infinite ordinal number. Some of the above symbols may be subscripted or have an over-tilde which will represent a finite sequence. For instance, x̃ stands for a sequence of the form (x1 , x2 , . . . ...
... ϑ a value assignment, or valuation, to a set of variables. As usual, the letter ω denotes the first infinite ordinal number. Some of the above symbols may be subscripted or have an over-tilde which will represent a finite sequence. For instance, x̃ stands for a sequence of the form (x1 , x2 , . . . ...
Logic in Nonmonotonic Reasoning
... continue to fail, because of the character of logistic in general rather than from defects of particular formalisms. According to Minsky, such a “logical” reasoning is not flexible enough to serve as a basis for thinking. Due to this deficiency, traditional logic cannot discuss what ought to be dedu ...
... continue to fail, because of the character of logistic in general rather than from defects of particular formalisms. According to Minsky, such a “logical” reasoning is not flexible enough to serve as a basis for thinking. Due to this deficiency, traditional logic cannot discuss what ought to be dedu ...