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thèse - IRIT
thèse - IRIT

... In the beginning of the 90s, Gelfond has introduced epistemic specifications (E-S) as an extension of disjunctive logic programming by epistemic notions. The underlying idea of E-S is to correctly reason about incomplete information, especially in situations when there are multiple answer sets. Rela ...
Proof Methods for Corecursive Programs
Proof Methods for Corecursive Programs

... clear that the dual but less well-known concept of corecursion is just as useful [1, 4, 20, 27]. Following the work of Moss and Danner [28] on the foundations of corecursion, we use the term corecursive program for a function whose range is a type defined recursively as the greatest solution of some ...
of Proof Methods for Corecursive Programs
of Proof Methods for Corecursive Programs

Types and Programming Languages
Types and Programming Languages

... x : U  x: U x : U  x : U T  App x : U  xx : T We can see that U must be of the form U  T but this is not possible (unless we have recursive types, which are coming later). ...
Lazy Evaluation in Numeric Computing
Lazy Evaluation in Numeric Computing

... – These attributes are computed out of the expression computation by outside control if it is necessity – Expression’s constituents with these operators are replaced by extraction needed items from corresponded attributes The direction to Vectors and Matrices expression is very promising ...
A logic-based theory of deductive arguments
A logic-based theory of deductive arguments

The Computer Modelling of Mathematical Reasoning Alan Bundy
The Computer Modelling of Mathematical Reasoning Alan Bundy

... theorem proving’ techniques could be readily brought into a Resolution framework, and how this helped us to relate the various techniques – creating coherence from confusion. In order to achieve this goal I have taken strong historical liberties in my descriptions of the work of Boyer and Moore, Gel ...
Notes on the Science of Logic
Notes on the Science of Logic

... without overwhelming you is that whenever a definition is justified, we feel free to employ it; but the justification itself, which is indeed an important matter for logic, is left for another course. We are furthermore compelled to say that there are some topics that we do not treat in these notes ...
Many-Valued Logic
Many-Valued Logic

... Bill Clinton regrets his affair with Margaret Thatcher. Bill Clinton does not regret his affair with Margaret Thatcher. ...
Provability as a Modal Operator with the models of PA as the Worlds
Provability as a Modal Operator with the models of PA as the Worlds

... iff A T (P ϕ), as desired. 3. Suppose ψ = ¬α, and by hypothesis M, A  α iff A T (α). Then MB , A  ¬α iff MB , Aα iff AT (α) iff A ¬T (α) iff A T (¬α), as desired. 4. Suppose ψ = α ∧ β and by hypothesis MB , A  α iff A T (α) and M, A  β iff A T (β). Then MB , A  α ∧ β iff MB , A  α and ...
The greatest common divisor: a case study for program extraction
The greatest common divisor: a case study for program extraction

... computation but just serves as a counter or more precisely as an upper bound for the number of steps until both remainders are zero. This will always happen if the induction principle is used only in the form of the least element principle (or, equivalently, <– induction) and the relation symbol < i ...
Higher-Order Functions for Parsing - Nottingham ePrints
Higher-Order Functions for Parsing - Nottingham ePrints

... For example, applying the parser (literal ’3’) to the string "345" gives the result [(’3’,"45")]. In the definition of literal, (=x) is a function which tests its argument for equality with x. It is an example of operator sectioning, a useful syntactic convention which allows us to partially apply i ...
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... the data, return the data without a change. quote becomes a list we can use A B instead of quote A B y Comments begin with a semicolon and continue until the end of line. define pi . bind a variable to a value y Scheme ignores the distinction between uppercase and lower case. y Names in scheme can h ...
Continuous Markovian Logic – From Complete ∗ Luca Cardelli
Continuous Markovian Logic – From Complete ∗ Luca Cardelli

... the degree of similarity of two systems in terms of their behaviours. For quantifying the behavioral similarity of probabilistic systems it has been introduced a class of pseudometrics [21, 6, 20]. In these settings, the distance between two processes is zero iff they are bisimilar; otherwise, they ...
Characterizations of stable model semantics for logic programs with
Characterizations of stable model semantics for logic programs with

... For instance, suppose we have a monotone constraint atom A1 = (D, 2D ). Semantically, this constraint atom is a tautology, since for any set I of atoms, it is a fact that I satisfies A1 , in the sense that I ∩ D ∈ 2D . A clever representation would just need to express two pieces of information, the ...
3. High-Level Functional Programming
3. High-Level Functional Programming

A Computationally-Discovered Simplification of the Ontological
A Computationally-Discovered Simplification of the Ontological

... P ıxF x, for the latter would be false when the description fails to denote (given a classical semantics for the description). By using free logic, we are prevented from substituting the description ‘that than which nothing greater can be conceived’ into universal claims without first establishing t ...
A Computationally-Discovered Simplification of the Ontological
A Computationally-Discovered Simplification of the Ontological

... P ıxF x, for the latter would be false when the description fails to denote (given a classical semantics for the description). By using free logic, we are prevented from substituting the description ‘that than which nothing greater can be conceived’ into universal claims without first establishing t ...
Teach Yourself Logic 2017: A Study Guide
Teach Yourself Logic 2017: A Study Guide

... daunting length. But there is another reason which I want to highlight: I very strongly recommend tackling an area of logic by reading a series of books which overlap in level (with the next one covering some of the same ground and then pushing on from the previous one), rather than trying to procee ...
C# is a functional programming language
C# is a functional programming language

... ◦ Type inference (for locals and lambdas) ◦ Streams (iterators) ◦ A library of higher-order functions for collections & iterators ◦ And even: GADTs (polymorphic inheritance) ...
Exact Bayesian Inference by Symbolic Disintegration
Exact Bayesian Inference by Symbolic Disintegration

... Whenever it reorders evaluation, it can produce a verification condition which identifies two integrals that have been exchanged. As long as the exchanges are correct, the disintegrator’s output is correct. ...
Teach Yourself Logic 2016: A Study Guide
Teach Yourself Logic 2016: A Study Guide

... daunting length. But there is another reason which I want to highlight: I very strongly recommend tackling an area of logic by reading a series of books which overlap in level (with the next one covering some of the same ground and then pushing on from the previous one), rather than trying to procee ...
Reading
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... is, strictly speaking, a distinct principle from HP, since HP = AX≈Y and HP2 = AY≈X (further, neither HP → HP2 nor HP2 → HP is a logical truth, since HP and HP2 involve distinct abstraction operators @X≈Y and @Y≈X). We shall address subtle issues regarding the equivalence of abstraction principles b ...
PPT - Crystal
PPT - Crystal

... List Patterns In Haskell, every non-empty list is constructed by repeated use of an operator : called “cons” that adds a new element to the start of a list. ...
Class Notes 2b: Scheme Reference
Class Notes 2b: Scheme Reference

... (equal? x y) is true if the values of x and y are the same object, maybe not atomic. (null? x) is true if x is (), the empty list. (append x y) concatenates the lists x and y. ...
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Combinatory logic

Combinatory logic is a notation to eliminate the need for quantified variables in mathematical logic. It was introduced by Moses Schönfinkel and Haskell Curry, and has more recently been used in computer science as a theoretical model of computation and also as a basis for the design of functional programming languages. It is based on combinators. A combinator is a higher-order function that uses only function application and earlier defined combinators to define a result from its arguments.
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