Critical Terminology for Theory of Knowledge
... believing that p independently of any evidence in favor of p provided by any other proposition that S believes. For example, a belief in a self-evident truth such as All squares are squares is basic for anyone who understands the meanings of the terms. But arguably not all basic beliefs are analytic ...
... believing that p independently of any evidence in favor of p provided by any other proposition that S believes. For example, a belief in a self-evident truth such as All squares are squares is basic for anyone who understands the meanings of the terms. But arguably not all basic beliefs are analytic ...
CHAPTER 1 INTRODUCTION 1 Mathematical Paradoxes
... a suitable set of axioms. If we do so, we obtain an axiomatic set theory without such antinomies. The problem arises what set of axioms should be chosen in order to obtain a sufficiently rich theory of sets. The first such axiomatic set theory was invented by Zermello in 1908. In chapter .. we shal ...
... a suitable set of axioms. If we do so, we obtain an axiomatic set theory without such antinomies. The problem arises what set of axioms should be chosen in order to obtain a sufficiently rich theory of sets. The first such axiomatic set theory was invented by Zermello in 1908. In chapter .. we shal ...
T - STI Innsbruck
... • Given the truth values of all symbols in a sentence, it can be “evaluated” to determine its truth value (True or False) • A model for a KB is a “possible world” (assignment of truth values to propositional symbols) in which each sentence in the KB is True • A valid sentence or tautology is a sente ...
... • Given the truth values of all symbols in a sentence, it can be “evaluated” to determine its truth value (True or False) • A model for a KB is a “possible world” (assignment of truth values to propositional symbols) in which each sentence in the KB is True • A valid sentence or tautology is a sente ...
02_Artificial_Intelligence-PropositionalLogic
... • Given the truth values of all symbols in a sentence, it can be “evaluated” to determine its truth value (True or False) • A model for a KB is a “possible world” (assignment of truth values to propositional symbols) in which each sentence in the KB is True • A valid sentence or tautology is a sente ...
... • Given the truth values of all symbols in a sentence, it can be “evaluated” to determine its truth value (True or False) • A model for a KB is a “possible world” (assignment of truth values to propositional symbols) in which each sentence in the KB is True • A valid sentence or tautology is a sente ...
F - Teaching-WIKI
... • Given the truth values of all symbols in a sentence, it can be “evaluated” to determine its truth value (True or False) • A model for a KB is a “possible world” (assignment of truth values to propositional symbols) in which each sentence in the KB is True • A valid sentence or tautology is a sente ...
... • Given the truth values of all symbols in a sentence, it can be “evaluated” to determine its truth value (True or False) • A model for a KB is a “possible world” (assignment of truth values to propositional symbols) in which each sentence in the KB is True • A valid sentence or tautology is a sente ...
A Proof Theory for Generic Judgments
... variables are called eigenvariables, and they are used to prove universally quantified formulas generically. In Gentzen’s original presentation of the sequent calculus [Gentzen 1969], eigenvariables are immutable during proof search: once an eigenvariable is introduced (reading proofs bottom-up), it ...
... variables are called eigenvariables, and they are used to prove universally quantified formulas generically. In Gentzen’s original presentation of the sequent calculus [Gentzen 1969], eigenvariables are immutable during proof search: once an eigenvariable is introduced (reading proofs bottom-up), it ...
On the Construction of Analytic Sequent Calculi for Sub
... is generalized in the current paper: (1) here we also consider derivations from assumptions (also known as “non-logical axioms”); and (2) we use a more general parametrized notion of a subformula. A particular well-behaved subfamily of pure calculi, called canonical calculi was studied in [4]. For t ...
... is generalized in the current paper: (1) here we also consider derivations from assumptions (also known as “non-logical axioms”); and (2) we use a more general parametrized notion of a subformula. A particular well-behaved subfamily of pure calculi, called canonical calculi was studied in [4]. For t ...
Document
... An argument in propositional logic is a sequence of propositions. All but the final proposition in the argument are called premises and the final proposition is called the conclusion. An argument is valid if the truth of all its premises implies that the conclusion is true. ...
... An argument in propositional logic is a sequence of propositions. All but the final proposition in the argument are called premises and the final proposition is called the conclusion. An argument is valid if the truth of all its premises implies that the conclusion is true. ...
Methods of Proof - Department of Mathematics
... Note that these methods are only general guidelines, every proof has its own form. The guts of the proof still needs to be filled in, these guidelines merely provide a possible staring point. Three Useful rules: 1. Always state what you are trying to prove in symbolic form first. 2. Always go back t ...
... Note that these methods are only general guidelines, every proof has its own form. The guts of the proof still needs to be filled in, these guidelines merely provide a possible staring point. Three Useful rules: 1. Always state what you are trying to prove in symbolic form first. 2. Always go back t ...
Chapter 2 Notes Niven – RHS Fall 12-13
... Inductive reasoning is when you find a pattern is specific cases and then write a conjecture for the general case. A conjecture is an unproven statement that is based on observations. Inductive reasoning boils down to analyzing a given set of data or observations, recognizing patterns, and making a ...
... Inductive reasoning is when you find a pattern is specific cases and then write a conjecture for the general case. A conjecture is an unproven statement that is based on observations. Inductive reasoning boils down to analyzing a given set of data or observations, recognizing patterns, and making a ...
methods of proof
... premises, continue with a sequence of deductions, and end with the conclusion. However, we will see that attempts at direct proofs often reach dead ends. We need other methods of proving theorems of the form ∀x(P(x) → Q(x)). Proofs of theorems of this type that are not direct proofs, that is, that d ...
... premises, continue with a sequence of deductions, and end with the conclusion. However, we will see that attempts at direct proofs often reach dead ends. We need other methods of proving theorems of the form ∀x(P(x) → Q(x)). Proofs of theorems of this type that are not direct proofs, that is, that d ...
A short article for the Encyclopedia of Artificial Intelligence: Second
... predicates, only quantification over individuals is permitted. Many concepts when translated into logic are, however, naturally expressed using quantifiers over functions and predicates. Leibniz’s principle of equality, for example, states that two objects are to be taken as equal if they share the ...
... predicates, only quantification over individuals is permitted. Many concepts when translated into logic are, however, naturally expressed using quantifiers over functions and predicates. Leibniz’s principle of equality, for example, states that two objects are to be taken as equal if they share the ...
Sub-Birkhoff
... =L = L∗ ∩ (L−1 )∗ . It is well-known (e.g. [1, Thm. 3.1.12]) that rewriting is logical in the sense that s is equal to t in equational logic iff s is convertible to t in the rewrite system induced by the specification. This extends to subequational logics (cf. [3, Lem. 2.6] for rewrite logic). Lemma ...
... =L = L∗ ∩ (L−1 )∗ . It is well-known (e.g. [1, Thm. 3.1.12]) that rewriting is logical in the sense that s is equal to t in equational logic iff s is convertible to t in the rewrite system induced by the specification. This extends to subequational logics (cf. [3, Lem. 2.6] for rewrite logic). Lemma ...
The Foundations: Logic and Proofs - UTH e
... Two compound propositions p and q are logically equivalent if p↔q is a tautology. We write this as p⇔q or as p≡q where p and q are compound propositions. Two compound propositions p and q are equivalent if and only if the columns in a truth table giving their truth values agree. This truth table sho ...
... Two compound propositions p and q are logically equivalent if p↔q is a tautology. We write this as p⇔q or as p≡q where p and q are compound propositions. Two compound propositions p and q are equivalent if and only if the columns in a truth table giving their truth values agree. This truth table sho ...
Propositional Logic: Part I - Semantics
... where m ≤ 2n and for i = 1, . . . n and j = 1, . . . m, xji is either pi or ¬pi E.g. (¬p ∨ ¬q ∨ r) ∧ (p ∨ ¬q ∨ ¬r) is in CNF ¬(p ∧ q) ∨ r is not. Each of the series of disjunctions rules out a row of the truth table where formula is false. CNF ANDs together the ORs for the false rows. One way to obt ...
... where m ≤ 2n and for i = 1, . . . n and j = 1, . . . m, xji is either pi or ¬pi E.g. (¬p ∨ ¬q ∨ r) ∧ (p ∨ ¬q ∨ ¬r) is in CNF ¬(p ∧ q) ∨ r is not. Each of the series of disjunctions rules out a row of the truth table where formula is false. CNF ANDs together the ORs for the false rows. One way to obt ...