Chapter 1 Logic and Set Theory
... The relation between intuition and formal rigor is not a trivial matter. Intuition tells us what is important, what might be true, and what mathematical tools may be used to prove it. Rigorous proofs are used to verify that a given statement that appears intuitively true is indeed true. Ultimately, ...
... The relation between intuition and formal rigor is not a trivial matter. Intuition tells us what is important, what might be true, and what mathematical tools may be used to prove it. Rigorous proofs are used to verify that a given statement that appears intuitively true is indeed true. Ultimately, ...
Predicate Logic
... • The domain of discourse U is all human beings. • “All human beings are mortal.” translates to x (H(x) M(x)) “Sachin is a human being.” translates to H(Sachin) • Therefore, for H(Sachin) M(Sachin) to be true it must be the case that M(Sachin). Later we will show this formally. Thursday, Januar ...
... • The domain of discourse U is all human beings. • “All human beings are mortal.” translates to x (H(x) M(x)) “Sachin is a human being.” translates to H(Sachin) • Therefore, for H(Sachin) M(Sachin) to be true it must be the case that M(Sachin). Later we will show this formally. Thursday, Januar ...
Introduction to proposition
... not a freshman.” Solution: There are many ways to translate this sentence into a logical expression. Although it is possible to represent the sentence by a single propositional variable, such as p, this would not be useful when analyzing its meaning or reasoning with it. Instead, we will use proposi ...
... not a freshman.” Solution: There are many ways to translate this sentence into a logical expression. Although it is possible to represent the sentence by a single propositional variable, such as p, this would not be useful when analyzing its meaning or reasoning with it. Instead, we will use proposi ...
How to tell the truth without knowing what you are talking about
... classification and categorization, modern logic is a calculus. In fact, in modern logic a symbolism must be devised, together with inference rules for manipulating symbols to discover new truths or to verify whether a conclusion can be derived from the premises. Today logic is considered a branch of ...
... classification and categorization, modern logic is a calculus. In fact, in modern logic a symbolism must be devised, together with inference rules for manipulating symbols to discover new truths or to verify whether a conclusion can be derived from the premises. Today logic is considered a branch of ...
Propositional Logic: Part I - Semantics
... Then f : R → R is the signature of f meaning f takes a real argument and produce a real. Here − is a unary prefix operator meaning it takes one argument, the number immediately following − (e.g., −(5) = −5). So really −:R→R Similarly + : R2 → R + is a binary operator on R so we could treat it as a p ...
... Then f : R → R is the signature of f meaning f takes a real argument and produce a real. Here − is a unary prefix operator meaning it takes one argument, the number immediately following − (e.g., −(5) = −5). So really −:R→R Similarly + : R2 → R + is a binary operator on R so we could treat it as a p ...
CA208ex1 - DCU School of Computing
... Kate is a student. If Kate is a student, then Kate is broke. |= Kate is broke. Kate is a student. Kate is broke. |= Kate is a student and Kate is broke. Kate is a student and Kate is broke. |= Kate is a student. Kate is a student. |= Kate is a student. Kate is taller than John. John is taller than M ...
... Kate is a student. If Kate is a student, then Kate is broke. |= Kate is broke. Kate is a student. Kate is broke. |= Kate is a student and Kate is broke. Kate is a student and Kate is broke. |= Kate is a student. Kate is a student. |= Kate is a student. Kate is taller than John. John is taller than M ...
Higher-Order Modal Logic—A Sketch
... Frege noted an analogous problem with intentional contexts, and introduced the notions of “sense” and “denotation” to deal with it. Roughly, this gives terms two kinds of values, what they denote, and what they mean. Of course this is loose. But the introduction of a scoping mechanism also turns out ...
... Frege noted an analogous problem with intentional contexts, and introduced the notions of “sense” and “denotation” to deal with it. Roughly, this gives terms two kinds of values, what they denote, and what they mean. Of course this is loose. But the introduction of a scoping mechanism also turns out ...
Introduction to logic
... We are going to deal with how to represent information in the KB and how to reason about it. We use logic as a device to pursue this aim. These notes are an introduction to modern logic, whose origin can be found in George Boole’s and Gottlob Frege’s works in the XIX century. However, logic in gener ...
... We are going to deal with how to represent information in the KB and how to reason about it. We use logic as a device to pursue this aim. These notes are an introduction to modern logic, whose origin can be found in George Boole’s and Gottlob Frege’s works in the XIX century. However, logic in gener ...
Mathematical Logic
... The truth table method is Exponential The problem of determining if a formula A containing n primitive propositions, is a logical consequence of the empty set, i.e., the problem of determining if A is valid, (|= A), takes an n-exponential number of steps. To check if A is a tautology, we have to con ...
... The truth table method is Exponential The problem of determining if a formula A containing n primitive propositions, is a logical consequence of the empty set, i.e., the problem of determining if A is valid, (|= A), takes an n-exponential number of steps. To check if A is a tautology, we have to con ...
