Propositional Logic: Part I - Semantics
... Let φ be some formula of propositional logic. In the case that |= φ, we say that φ is valid. In the case that φ is not valid (i.e., there is some assignment to its variables that makes it false) we will write 6|= φ. If there is some assignment to the propositional variables that makes φ true (i.e., ...
... Let φ be some formula of propositional logic. In the case that |= φ, we say that φ is valid. In the case that φ is not valid (i.e., there is some assignment to its variables that makes it false) we will write 6|= φ. If there is some assignment to the propositional variables that makes φ true (i.e., ...
Principles of Programming Languages
... Programming , Logic Programming. Programming Language Implementation – Compilation and Virtual Machines, programming environments. UNIT – II: Syntax and Semantics: general Problem of describing Syntax and Semantics, formal methods of describing syntax - BNF, EBNF for common programming languages fea ...
... Programming , Logic Programming. Programming Language Implementation – Compilation and Virtual Machines, programming environments. UNIT – II: Syntax and Semantics: general Problem of describing Syntax and Semantics, formal methods of describing syntax - BNF, EBNF for common programming languages fea ...
Functional Languages and Higher
... – Type inference is like type checking but no type declarations are required • Types of variables and expressions can be inferred from context ...
... – Type inference is like type checking but no type declarations are required • Types of variables and expressions can be inferred from context ...
Thursday Feb 9, at 1:00
... We first rename the variable on the right hand side as y to get ∃xP (x) → ∃yQ(y). We rewrite the statement by reinterpreting implication as ¬∃xP (x) ∨ ∃yQ(y)). Then by moving the negation in front of the predicate P (x) gives us ∀x¬P (x) ∨ ∃yQ(y). Now by 49(b), we can rewrite this as ∀x∃y(¬P (x) ∨ Q ...
... We first rename the variable on the right hand side as y to get ∃xP (x) → ∃yQ(y). We rewrite the statement by reinterpreting implication as ¬∃xP (x) ∨ ∃yQ(y)). Then by moving the negation in front of the predicate P (x) gives us ∀x¬P (x) ∨ ∃yQ(y). Now by 49(b), we can rewrite this as ∀x∃y(¬P (x) ∨ Q ...
Analysis of the paraconsistency in some logics
... contains ¬ as negation symbol, whether it is defined or native, besides some other logic symbols proper of each theory. Initially, as we have already said, we consider our logics with a consequence relation satisfying Con1, Con2 y Con3, but this does not mean that every consequence relation satisfie ...
... contains ¬ as negation symbol, whether it is defined or native, besides some other logic symbols proper of each theory. Initially, as we have already said, we consider our logics with a consequence relation satisfying Con1, Con2 y Con3, but this does not mean that every consequence relation satisfie ...
Curry`s Paradox. An Argument for Trivialism
... A being a dialetheia should lead dialetheists to reject the classical equivalence between (A→ B) and (¬A ∨ B). This equivalence holds in classical logic because the truth of (¬A ∨ B) guarantees that truth is preserved from A to B for the reason that dialetheiae are excluded. Of course, nothing preve ...
... A being a dialetheia should lead dialetheists to reject the classical equivalence between (A→ B) and (¬A ∨ B). This equivalence holds in classical logic because the truth of (¬A ∨ B) guarantees that truth is preserved from A to B for the reason that dialetheiae are excluded. Of course, nothing preve ...
Lesson 12
... Notes: 1. A, B are not formulas, but meta-symbols denoting any formula. Each axiom schema denotes an infinite class of formulas of a given form. If axioms were specified by concrete formulas, like 1. p (q p) 2. (p (q r)) ((p q) (p r)) 3. (q p) (p q) we would have to extend th ...
... Notes: 1. A, B are not formulas, but meta-symbols denoting any formula. Each axiom schema denotes an infinite class of formulas of a given form. If axioms were specified by concrete formulas, like 1. p (q p) 2. (p (q r)) ((p q) (p r)) 3. (q p) (p q) we would have to extend th ...
CSE 341 - Unit 4
... might be putting this code up on the internet for people to use. I want to be able to think about could I replace this function with this other function without any possible call to these functions ever being able to tell. That's what equivalence is all about. [00:02:30.65] Now, we need to define wh ...
... might be putting this code up on the internet for people to use. I want to be able to think about could I replace this function with this other function without any possible call to these functions ever being able to tell. That's what equivalence is all about. [00:02:30.65] Now, we need to define wh ...
A Logic of Explicit Knowledge - Lehman College
... Now we drop the operator K from the language, and introduce a family of explicit reasons instead— I’ll use t as a typical one. Following [1, 2] I’ll write t:X to indicate that t applies to X—read it as “X is known for reason t.” Formally, if t is a reason and X is a formula, t:X is a formula. Of cou ...
... Now we drop the operator K from the language, and introduce a family of explicit reasons instead— I’ll use t as a typical one. Following [1, 2] I’ll write t:X to indicate that t applies to X—read it as “X is known for reason t.” Formally, if t is a reason and X is a formula, t:X is a formula. Of cou ...
Chapter 5 THE LAMBDA CALCULUS
... unctions play a prominent role in describing the semantics of a programming language, since the meaning of a computer program can be considered as a function from input values to output values. In addition, functions play an essential role in mathematics, which means that much of the theory of funct ...
... unctions play a prominent role in describing the semantics of a programming language, since the meaning of a computer program can be considered as a function from input values to output values. In addition, functions play an essential role in mathematics, which means that much of the theory of funct ...
To What Type of Logic Does the "Tetralemma" Belong?
... related to the distinction between what, using a different language, might have been called “positive” and “negative” propositions. Consider the (“unasserted”) propositions, A = “the electron is here” and Ā = “the electron is elsewhere”. A statement like “I see the electron here” is in some sense po ...
... related to the distinction between what, using a different language, might have been called “positive” and “negative” propositions. Consider the (“unasserted”) propositions, A = “the electron is here” and Ā = “the electron is elsewhere”. A statement like “I see the electron here” is in some sense po ...
A simplified form of condensed detachment - Research Online
... (m.g.u) of a and ft if every other unification of a and /? is a substitution instance ofa(a). A substitution a is said to be alphabetic*relative to a formula a, if it replaces all or some of the variables in a by variablesdistinct from each other and from any variables in a that are not replaced. N ...
... (m.g.u) of a and ft if every other unification of a and /? is a substitution instance ofa(a). A substitution a is said to be alphabetic*relative to a formula a, if it replaces all or some of the variables in a by variablesdistinct from each other and from any variables in a that are not replaced. N ...
Logic - Disclaimer
... Parentheses and Ambiguity • An ambiguous statements is a statement whose meaning is not clear due to its syntax. Example : ”P or Q and R” • In formal systems, an expression like P Q R is simply not allowed and considered unsyntactical. • Claims in our formal language are therefore never ambiguo ...
... Parentheses and Ambiguity • An ambiguous statements is a statement whose meaning is not clear due to its syntax. Example : ”P or Q and R” • In formal systems, an expression like P Q R is simply not allowed and considered unsyntactical. • Claims in our formal language are therefore never ambiguo ...
Introducing Quantified Cuts in Logic with Equality
... size of a decomposition U ◦ᾱ W is |U | + |W |. When it is clear that the variables in question are α1 , . . . , αm , we just write U ◦ W . In [7], we gave an algorithm that treated the special case where m = 1. Here, we will extend that approach with a generalized Δ-vector ΔG , which, together with ...
... size of a decomposition U ◦ᾱ W is |U | + |W |. When it is clear that the variables in question are α1 , . . . , αm , we just write U ◦ W . In [7], we gave an algorithm that treated the special case where m = 1. Here, we will extend that approach with a generalized Δ-vector ΔG , which, together with ...
Chapter 15 - Department of Computer Science University of Miami
... • It is strongly typed (whereas Scheme is essentially typeless) and has no type coercions ...
... • It is strongly typed (whereas Scheme is essentially typeless) and has no type coercions ...
Functional programming languages
... Lambda expressions are applied to parameter(s) by placing the parameter(s) after the expression, as in ((x) x * x * x)(3) ...
... Lambda expressions are applied to parameter(s) by placing the parameter(s) after the expression, as in ((x) x * x * x)(3) ...
lectur15
... Lambda expressions are applied to parameter(s) by placing the parameter(s) after the expression, as in ((x) x * x * x)(3) ...
... Lambda expressions are applied to parameter(s) by placing the parameter(s) after the expression, as in ((x) x * x * x)(3) ...
Autoepistemic Logic and Introspective Circumscription
... Thus, technically, the two systems appear to be quite different, and introspective circumscription, the younger and less known of the two, may have important advantages. The ease with which it handles quantification and equality is, in particular, of interest to logic programming. Since autoepistemi ...
... Thus, technically, the two systems appear to be quite different, and introspective circumscription, the younger and less known of the two, may have important advantages. The ease with which it handles quantification and equality is, in particular, of interest to logic programming. Since autoepistemi ...
