Lectures on Proof Theory - Create and Use Your home.uchicago
... of the principles of logic to be used in deriving theorems from the axioms, so that logic itself could be axiomatized. In this case, too, the timing was just right: the analysis of logic in Frege’s Begriffsschrift was just what was required. (There was a remarkable meeting here of supply and demand. ...
... of the principles of logic to be used in deriving theorems from the axioms, so that logic itself could be axiomatized. In this case, too, the timing was just right: the analysis of logic in Frege’s Begriffsschrift was just what was required. (There was a remarkable meeting here of supply and demand. ...
Introduction to Mathematical Logic
... By the widely accepted definition logic investigates the laws, and methods of inference and argumentation. Mathematical logic is a mathematical investigation of this subject, similarly as number theory is the mathematical investigation of the natural numbers. Developing such a theory one can use the ...
... By the widely accepted definition logic investigates the laws, and methods of inference and argumentation. Mathematical logic is a mathematical investigation of this subject, similarly as number theory is the mathematical investigation of the natural numbers. Developing such a theory one can use the ...
Discrete Mathematics
... declarative sentence) with a definite meaning, having a truth value that’s either true (T) or false (F) (never both, neither, or somewhere in between). A proposition (statement) may be denoted by a variable like P, Q, R,…, called a proposition (statement) variable. ...
... declarative sentence) with a definite meaning, having a truth value that’s either true (T) or false (F) (never both, neither, or somewhere in between). A proposition (statement) may be denoted by a variable like P, Q, R,…, called a proposition (statement) variable. ...
Document
... • there are infinitely many of them, based on different tautologies • validity of an argument form can be verified e.g. using truth tables There are simple, commonly used and useful argument forms • when writing proofs for humans, it is good to use well known argument forms • so that the reader can ...
... • there are infinitely many of them, based on different tautologies • validity of an argument form can be verified e.g. using truth tables There are simple, commonly used and useful argument forms • when writing proofs for humans, it is good to use well known argument forms • so that the reader can ...
THE AXIOM SCHEME OF ACYCLIC COMPREHENSION keywords
... This observation allows us to ignore identifications between occurrences of constants in judging whether a formula can be used to define a set, because we can generalize a definition containing a constant by replacing each occurrence of the constant with a different free variable. (By “constant” we ...
... This observation allows us to ignore identifications between occurrences of constants in judging whether a formula can be used to define a set, because we can generalize a definition containing a constant by replacing each occurrence of the constant with a different free variable. (By “constant” we ...
Chapter 3 Proof
... his guilt to be proven. When scientists find that a theory has passed numerous empirical tests, it is taken as proved. We make do with something less than logical certainty in these contexts because there is no alternative. Mathematicians, however, do have an alternative. In mathematics we demand lo ...
... his guilt to be proven. When scientists find that a theory has passed numerous empirical tests, it is taken as proved. We make do with something less than logical certainty in these contexts because there is no alternative. Mathematicians, however, do have an alternative. In mathematics we demand lo ...
The Dedekind Reals in Abstract Stone Duality
... terms of their universal properties. (Recall that, classically, the Sierpiński space has one open and one closed point.) We can form products of spaces, X × Y , and exponentials of the form ΣX , but not arbitrary Y X . The theory also provides certain “Σ-split” subspaces, which we explain with refe ...
... terms of their universal properties. (Recall that, classically, the Sierpiński space has one open and one closed point.) We can form products of spaces, X × Y , and exponentials of the form ΣX , but not arbitrary Y X . The theory also provides certain “Σ-split” subspaces, which we explain with refe ...
F - Teaching-WIKI
... conclusions) from statements that are assumed to be true (called premises) • Natural language is not precise, so the careless use of logic can lead to claims that false statements are true, or to claims that a statement is true, even tough its truth does not necessarily follow from the premises => L ...
... conclusions) from statements that are assumed to be true (called premises) • Natural language is not precise, so the careless use of logic can lead to claims that false statements are true, or to claims that a statement is true, even tough its truth does not necessarily follow from the premises => L ...
A proof
... first step is the assumption that p is true; subsequent steps are constructed using rules of inference, with the final step showing that q must also be true. • A direct proof shows that a conditional statement pq is true by showing that if p is true then q must also be true. • In a direct proof, we ...
... first step is the assumption that p is true; subsequent steps are constructed using rules of inference, with the final step showing that q must also be true. • A direct proof shows that a conditional statement pq is true by showing that if p is true then q must also be true. • In a direct proof, we ...
And this is just one theorem prover!
... the correctness of the software itself, but also of all the artifacts needed to execute the software (e.g. ...
... the correctness of the software itself, but also of all the artifacts needed to execute the software (e.g. ...
