powerpoint - IDA.LiU.se
... all those that occur in the formula (and maybe some more) Interpretation for a logic formula: a mapping from a vocabulary for it, to truth-values T or F Model for a logic formula: an interpretation where the value of the formula is T Joint vocabulary for two (or more) logic formulas: something that ...
... all those that occur in the formula (and maybe some more) Interpretation for a logic formula: a mapping from a vocabulary for it, to truth-values T or F Model for a logic formula: an interpretation where the value of the formula is T Joint vocabulary for two (or more) logic formulas: something that ...
Normalised and Cut-free Logic of Proofs
... From a Gentzen-style point of view, we can formulate two similar sequent calculi for the two systems Lp and Ilp, respectively (see Artemov [2002]). Although simple and cut-free, these sequent calculi fail to satisfy certain properties that are standardly required from a “good" sequent calculus (in P ...
... From a Gentzen-style point of view, we can formulate two similar sequent calculi for the two systems Lp and Ilp, respectively (see Artemov [2002]). Although simple and cut-free, these sequent calculi fail to satisfy certain properties that are standardly required from a “good" sequent calculus (in P ...
PowerPoint - School of Computing Science
... We have functions, e.g. x.x+2 is a function, but can we really do functional programming? It’s essential to be able to define recursive functions, but our language has no direct support for recursive definitions. We have no way of associating a name with a function. It is possible to express namele ...
... We have functions, e.g. x.x+2 is a function, but can we really do functional programming? It’s essential to be able to define recursive functions, but our language has no direct support for recursive definitions. We have no way of associating a name with a function. It is possible to express namele ...
EECS 203-1 – Winter 2002 Definitions review sheet
... it is true for all possible assignments of truth values to its variables. A contradictory expression is false for all assignments of truth values to its variables. A satisfiable formula is an expression which is true for at least one assignment. • Logical equivalence and implication in propositional ...
... it is true for all possible assignments of truth values to its variables. A contradictory expression is false for all assignments of truth values to its variables. A satisfiable formula is an expression which is true for at least one assignment. • Logical equivalence and implication in propositional ...
Lambda
... (x. y. (+ x y)) 3 5 A 2-parameter function is simulated with two 1parameter functions. The result of applying the first function is another function. This new function accepts the second argument and produces the result of the simulated 2-parameter function. More parameters can be handled similarl ...
... (x. y. (+ x y)) 3 5 A 2-parameter function is simulated with two 1parameter functions. The result of applying the first function is another function. This new function accepts the second argument and produces the result of the simulated 2-parameter function. More parameters can be handled similarl ...
1
... • ∀x((∃yRxy→Ax)→Bxy), • ∀x(Ax→∃yBy) ∧ ∃z(Cxz→∃xDxyz). (b) Give the definition of a atomic formula of predicate logic and of a valuation of terms s based on a variable assignment s. (c) Prove the following by induction (on construction of formulas): if variable assignments s and s0 agree on all varia ...
... • ∀x((∃yRxy→Ax)→Bxy), • ∀x(Ax→∃yBy) ∧ ∃z(Cxz→∃xDxyz). (b) Give the definition of a atomic formula of predicate logic and of a valuation of terms s based on a variable assignment s. (c) Prove the following by induction (on construction of formulas): if variable assignments s and s0 agree on all varia ...
Untyped Lambda Calculus - Programming Systems Lab
... Given two terms s and t, we say that s evaluates to t and write s ⇓ t if s ∗ t and t is normal. If s evaluates to t, we say that t is a normal form of s. Note that the combinator Ω has no normal form. A main result about the lambda calculus says that every term has at most one normal form. An inter ...
... Given two terms s and t, we say that s evaluates to t and write s ⇓ t if s ∗ t and t is normal. If s evaluates to t, we say that t is a normal form of s. Note that the combinator Ω has no normal form. A main result about the lambda calculus says that every term has at most one normal form. An inter ...
Functional Programming
... What is a Functional Language? Opinions differ, and it is difficult to give a precise definition, but generally speaking: Functional programming is style of programming in which the basic method of computation is the application of functions to arguments; ...
... What is a Functional Language? Opinions differ, and it is difficult to give a precise definition, but generally speaking: Functional programming is style of programming in which the basic method of computation is the application of functions to arguments; ...
coppin chapter 07e
... If a statement A is contingent then we say that A is possibly true, which is written: ◊A If A is non-contingent, then it is necessarily true, which is written: A ...
... If a statement A is contingent then we say that A is possibly true, which is written: ◊A If A is non-contingent, then it is necessarily true, which is written: A ...
pdf
... incompleteness theorem, and it led to his predictions about machine intelligence and his famous Turing test for intelligence. He agreed with Leibniz that the mind works by computation. On the other hand, Turing’s work raised the question of whether human computation (“effective computation”) is the ...
... incompleteness theorem, and it led to his predictions about machine intelligence and his famous Turing test for intelligence. He agreed with Leibniz that the mind works by computation. On the other hand, Turing’s work raised the question of whether human computation (“effective computation”) is the ...
IntroToLogic - Department of Computer Science
... The validity of first order logic is not decidable. (It is semi-decidable.) If a theorem is logically entailed by an axiom, you can prove that it is. But if it is not, you can’t necessarily prove that it is not. (You may go on infinitely with your ...
... The validity of first order logic is not decidable. (It is semi-decidable.) If a theorem is logically entailed by an axiom, you can prove that it is. But if it is not, you can’t necessarily prove that it is not. (You may go on infinitely with your ...
Different notions of conuity and intensional models for λ
... P a generalized sequence of its elements (i.e. a sequence with directed set of indexes, not necessarily equal to the set of naturals). Then, in the case if P is increasing (decreasing), we define its limit as the least upper bound (the greatest lower bound) of its elements. In the general case, we p ...
... P a generalized sequence of its elements (i.e. a sequence with directed set of indexes, not necessarily equal to the set of naturals). Then, in the case if P is increasing (decreasing), we define its limit as the least upper bound (the greatest lower bound) of its elements. In the general case, we p ...
Lambda Calculus and Lisp
... lambda, period, parentheses and numbers. • M -> x | (M M) | x.M • If F and A are both expressions then so is (F A) and indicates the application of the function F with A as its parameter. • If F is a expression then so is x.F This is a function definition and is also called an ABSTRACTION beca ...
... lambda, period, parentheses and numbers. • M -> x | (M M) | x.M • If F and A are both expressions then so is (F A) and indicates the application of the function F with A as its parameter. • If F is a expression then so is x.F This is a function definition and is also called an ABSTRACTION beca ...
Programming and Problem Solving with Java: Chapter 14
... If a statement A is contingent then we say that A is possibly true, which is written: ◊A If A is non-contingent, then it is necessarily true, which is written: A ...
... If a statement A is contingent then we say that A is possibly true, which is written: ◊A If A is non-contingent, then it is necessarily true, which is written: A ...
Compiling Functional Programming Languages (FPLs) λ
... Combinators: A lambda expression with no occcurences of a free variable. Combinators have by convention names, such as B , S , K , I , C , T etc. Less than a handful is enough to write ANY lambda expression (assuming no free variables) WITHOUT VARIABLES, as Curry and Feys showed in 1958. Amazingly, ...
... Combinators: A lambda expression with no occcurences of a free variable. Combinators have by convention names, such as B , S , K , I , C , T etc. Less than a handful is enough to write ANY lambda expression (assuming no free variables) WITHOUT VARIABLES, as Curry and Feys showed in 1958. Amazingly, ...
Functional Programming
... thing and the thing itself (e.g., call-by-value and call-by-reference are the same). • The order in which expressions are evaluated is not important; neither is the place of their occurrence in the source code. • The program will yield the same output on the same input in any evaluation order: deter ...
... thing and the thing itself (e.g., call-by-value and call-by-reference are the same). • The order in which expressions are evaluated is not important; neither is the place of their occurrence in the source code. • The program will yield the same output on the same input in any evaluation order: deter ...
curry
... two arguments of types a and b and returns a value of type c like this: – g :: (a, b) -> c • We can let f be the curried form of g by – f = curry g • The function f now has the signature – f :: a -> b -> c • f takes an arg of type a & returns a function that takes an arg of type b & returns a value ...
... two arguments of types a and b and returns a value of type c like this: – g :: (a, b) -> c • We can let f be the curried form of g by – f = curry g • The function f now has the signature – f :: a -> b -> c • f takes an arg of type a & returns a function that takes an arg of type b & returns a value ...
Propositional Logic Predicate Logic
... Name of Symbols ∀ (universal quantifier), and ∃ (existential quantifier). Definition. A formula A is valid if A is true no matter how we replace the individual constants in A with concrete individuals and the predicate variables in A with concrete predicates. Note. The set of individuals must be in ...
... Name of Symbols ∀ (universal quantifier), and ∃ (existential quantifier). Definition. A formula A is valid if A is true no matter how we replace the individual constants in A with concrete individuals and the predicate variables in A with concrete predicates. Note. The set of individuals must be in ...
