Theories and uses of context in knowledge representation and
... • given a (global) representation language L, the facts that are true in a given context c can be isolated (“localized”) and treated as a distinct collection of facts with respect to the facts belonging to different contexts; • there are hierarchical relations between contexts that allow reasoning t ...
... • given a (global) representation language L, the facts that are true in a given context c can be isolated (“localized”) and treated as a distinct collection of facts with respect to the facts belonging to different contexts; • there are hierarchical relations between contexts that allow reasoning t ...
Relevant deduction
... also be applied to inductive reasoning.2 Although there has been considerable progress in realizing the program of Analytic Philosophy since the time of its founders, the enterprise of reconstructing philosophical concepts and principles within a system of exact symbolic logic has always been confro ...
... also be applied to inductive reasoning.2 Although there has been considerable progress in realizing the program of Analytic Philosophy since the time of its founders, the enterprise of reconstructing philosophical concepts and principles within a system of exact symbolic logic has always been confro ...
Math 13 — An Introduction to Abstract Mathematics
... In elementary school you largely learn arithmetic and the basic notions of shape. This is the mathematics all of us need in order to function in the real world. If you don’t know the difference between 15,000 and 150,000, you probably shouldn’t try to buy a new car! For the vast majority of people, ...
... In elementary school you largely learn arithmetic and the basic notions of shape. This is the mathematics all of us need in order to function in the real world. If you don’t know the difference between 15,000 and 150,000, you probably shouldn’t try to buy a new car! For the vast majority of people, ...
Provability as a Modal Operator with the models of PA as the Worlds
... ψ1 D M ψ2 then ¬ψ1 D M ¬ψ2 and α ∧ ψ1 D M α ∧ ψ2 and ψ1 ∧ α D M ψ2 ∧ α and α → ψ1 D M α → ψ2 and ψ1 → α D M ψ2 → α and 2ψ1 D M 2ψ2 and [ψ1]α D M [ψ2]α. This implies that as long as a sub-formula is not on the right hand side of an announement operator, it can be replaced with an equivalent sub-formu ...
... ψ1 D M ψ2 then ¬ψ1 D M ¬ψ2 and α ∧ ψ1 D M α ∧ ψ2 and ψ1 ∧ α D M ψ2 ∧ α and α → ψ1 D M α → ψ2 and ψ1 → α D M ψ2 → α and 2ψ1 D M 2ψ2 and [ψ1]α D M [ψ2]α. This implies that as long as a sub-formula is not on the right hand side of an announement operator, it can be replaced with an equivalent sub-formu ...
The Computer Modelling of Mathematical Reasoning Alan Bundy
... techniques or programs. Each was selected because it contributes an important partial solution to the problem of guiding the search for a proof. This part is the heart of the book. • Part IV is a two chapter discussion of aspects of mathematical reasoning other than proving theorems – although they ...
... techniques or programs. Each was selected because it contributes an important partial solution to the problem of guiding the search for a proof. This part is the heart of the book. • Part IV is a two chapter discussion of aspects of mathematical reasoning other than proving theorems – although they ...
Chapter4
... factorizations is not efficient because there is no efficient algorithm for finding the prime factorization of a positive integer. ...
... factorizations is not efficient because there is no efficient algorithm for finding the prime factorization of a positive integer. ...
AN INVITATION TO ADDITIVE PRIME NUMBER THEORY A. V.
... of kth powers, the sequence of prime numbers, the values taken by a polynomial F (X) ∈ Z[X] at the positive integers or at the primes, etc.). In this survey, we discuss almost exclusively problems of the latter kind. The main focus will be on two questions, known as Goldbach’s problem and the Waring ...
... of kth powers, the sequence of prime numbers, the values taken by a polynomial F (X) ∈ Z[X] at the positive integers or at the primes, etc.). In this survey, we discuss almost exclusively problems of the latter kind. The main focus will be on two questions, known as Goldbach’s problem and the Waring ...
Chapter 10 Number Theory and Cryptography
... reducing each of its subexpressions modulo n produces the same result as computing the entire expression and then reducing that value modulo n. Also, every element x in Zn has an additive inverse, that is, for each x ∈ Zn , there is a y ∈ Zn such that x + y mod n = 0. For example, the additive inver ...
... reducing each of its subexpressions modulo n produces the same result as computing the entire expression and then reducing that value modulo n. Also, every element x in Zn has an additive inverse, that is, for each x ∈ Zn , there is a y ∈ Zn such that x + y mod n = 0. For example, the additive inver ...
Fibonacci numbers that are not sums of two prime powers
... then Fn 6= pa + q b with p, q prime numbers and a, b nonnegative integers. We use the same method employed in [2, 3, 9]. However, there are additional difficulties which arise because we want our numbers to belong to the Fibonacci sequence. Let us quickly recall how one can create a residue class of ...
... then Fn 6= pa + q b with p, q prime numbers and a, b nonnegative integers. We use the same method employed in [2, 3, 9]. However, there are additional difficulties which arise because we want our numbers to belong to the Fibonacci sequence. Let us quickly recall how one can create a residue class of ...