higher-order logic - University of Amsterdam
... In addition to its primitives all and some, a first-order predicate language with identity can also express such quantifiers as precisely one, all but two, at most three, etcetera, referring to specific finite quantities. What is lacking, however, is the general mathematical concept of finiteness. E ...
... In addition to its primitives all and some, a first-order predicate language with identity can also express such quantifiers as precisely one, all but two, at most three, etcetera, referring to specific finite quantities. What is lacking, however, is the general mathematical concept of finiteness. E ...
A Proof Theory for Generic Judgments
... that the sequent Γ0 , ∀xB −→ C is proved using the introduction of ∀ on the left from the premise Γ0 , B[t/x] −→ C, where t is some term. To reduce the rank of the cut formula ∀x.B between the sequents Γ −→ ∀x.B and Γ0 , ∀xB −→ C, the eigenvariable c in the sequent calculus proof Π(c) must be substi ...
... that the sequent Γ0 , ∀xB −→ C is proved using the introduction of ∀ on the left from the premise Γ0 , B[t/x] −→ C, where t is some term. To reduce the rank of the cut formula ∀x.B between the sequents Γ −→ ∀x.B and Γ0 , ∀xB −→ C, the eigenvariable c in the sequent calculus proof Π(c) must be substi ...
KRR Lectures — Contents
... A proposition is an expression of a fact. The symbols, P and Q, represent propositions and the logical symbol ‘ → ’ is called a propositional connective. Many systems of propositional logic have been developed. In this lecture we are studying classical — i.e. the best established — propositional log ...
... A proposition is an expression of a fact. The symbols, P and Q, represent propositions and the logical symbol ‘ → ’ is called a propositional connective. Many systems of propositional logic have been developed. In this lecture we are studying classical — i.e. the best established — propositional log ...
Introduction to Discrete Structures Introduction
... A and B, denoted AxB, is the set of all ordered pairs (a,b) where aA and bB AxB={ (a,b) | (aA) (b B) } • The Cartesian product is also known as the cross product • Definition: A subset of a Cartesian product, R AxB is called a relation. We will talk more abot relations in the next set of sl ...
... A and B, denoted AxB, is the set of all ordered pairs (a,b) where aA and bB AxB={ (a,b) | (aA) (b B) } • The Cartesian product is also known as the cross product • Definition: A subset of a Cartesian product, R AxB is called a relation. We will talk more abot relations in the next set of sl ...
Logic
... P(x): If x is even, then x 2 is even. Q(x): x is even. R(x, y ): x < y . Here P(x) is a statement with a variable x. It is always true, regardless of the value of x. The truth of Q(x), however, depends on the value of x. This is called a propositional function or an open sentence. More than one vari ...
... P(x): If x is even, then x 2 is even. Q(x): x is even. R(x, y ): x < y . Here P(x) is a statement with a variable x. It is always true, regardless of the value of x. The truth of Q(x), however, depends on the value of x. This is called a propositional function or an open sentence. More than one vari ...
Quadripartitaratio - Revistas Científicas de la Universidad de
... make the use-mention distinction: the seven-character name ‘(2 + 3)’ isn’t the one-character name ‘5’, but they name the same number—which some people might regard as a kind of equality. Tarski ...
... make the use-mention distinction: the seven-character name ‘(2 + 3)’ isn’t the one-character name ‘5’, but they name the same number—which some people might regard as a kind of equality. Tarski ...
A pragmatic dialogic interpretation of bi
... involves a choice between the disjuncts. Following Girard’s classification of connectives in linear logic [27], it is the additive form of intuitionistic disjunction that makes it an unsuitable candidate as a right adjoint of subtraction. The solution advocated in [11] is to take multiplicative disj ...
... involves a choice between the disjuncts. Following Girard’s classification of connectives in linear logic [27], it is the additive form of intuitionistic disjunction that makes it an unsuitable candidate as a right adjoint of subtraction. The solution advocated in [11] is to take multiplicative disj ...
FLP Semantics Without Circular Justifications for General Logic
... by itself. Our study shows that the key reason behind the circular justification problem for general logic programs is that the FLP semantics is unable to build a level mapping on its answer sets. Such a level mapping is defined implicitly by rules of a logic program such that answers at upper level ...
... by itself. Our study shows that the key reason behind the circular justification problem for general logic programs is that the FLP semantics is unable to build a level mapping on its answer sets. Such a level mapping is defined implicitly by rules of a logic program such that answers at upper level ...
Chapter 18
... Uses less expensive hardware Handles control or decision-making problems not easily defined by mathematical models ...
... Uses less expensive hardware Handles control or decision-making problems not easily defined by mathematical models ...
Propositional Logic and Methods of Inference
... The basic idea of normal form is to express wffs in a standard form that uses only the ^, v, and possibly ~ The resolution method is then applied to normal form wffs in which all other connectives and quantifiers have been eliminated Resolution is an operation on pairs of disjuncts, which produces n ...
... The basic idea of normal form is to express wffs in a standard form that uses only the ^, v, and possibly ~ The resolution method is then applied to normal form wffs in which all other connectives and quantifiers have been eliminated Resolution is an operation on pairs of disjuncts, which produces n ...
Truth-Functional Propositional Logic
... true (these statements are mutually inconsistent), it is possible for both of them to be false. In the standard nomenclature, contraries are mutually exclusive (mutually inconsistent) not collectively exhaustive. In contrast, contradictories are both mutually exclusive and collectively exhaustive. G ...
... true (these statements are mutually inconsistent), it is possible for both of them to be false. In the standard nomenclature, contraries are mutually exclusive (mutually inconsistent) not collectively exhaustive. In contrast, contradictories are both mutually exclusive and collectively exhaustive. G ...
Fuzzy logic
Fuzzy logic is a form of many-valued logic in which the truth values of variables may be any real number between 0 and 1. By contrast, in Boolean logic, the truth values of variables may only be 0 or 1. Fuzzy logic has been extended to handle the concept of partial truth, where the truth value may range between completely true and completely false. Furthermore, when linguistic variables are used, these degrees may be managed by specific functions.The term fuzzy logic was introduced with the 1965 proposal of fuzzy set theory by Lotfi A. Zadeh. Fuzzy logic has been applied to many fields, from control theory to artificial intelligence. Fuzzy logic had however been studied since the 1920s, as infinite-valued logic—notably by Łukasiewicz and Tarski.