Search results
Results from the WOW.Com Content Network
Proof theory is a major branch [1] of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures such as lists, boxed lists, or trees, which are constructed ...
Barwise, along with his former colleague at Stanford John Etchemendy, was the author of the popular logic textbook Language, Proof and Logic. Unlike the Handbook of Mathematical Logic, which was a survey of the state of the art of mathematical logic circa 1975, and of which he was the editor, this work targeted elementary logic. The text is ...
A classic question in philosophy asks whether mathematical proofs are analytic or synthetic. Kant, who introduced the analytic–synthetic distinction, believed mathematical proofs are synthetic, whereas Quine argued in his 1951 "Two Dogmas of Empiricism" that such a distinction is untenable. [13] Proofs may be admired for their mathematical ...
The use of "Hilbert-style" and similar terms to describe axiomatic proof systems in logic is due to the influence of Hilbert and Ackermann's Principles of Mathematical Logic (1928). [2] Most variants of Hilbert systems take a characteristic tack in the way they balance a trade-off between logical axioms and rules of inference.
Language, Proof and Logic is an educational software package, devised and written by Jon Barwise and John Etchemendy, geared to teaching formal logic through the use of a tight integration between a textbook (same name as the package) and four software programs, where three of them are logic related (Boole, Fitch and Tarski's World) and the other (Submit) is an internet-based grading service.
In mathematical logic, Lindström's theorem (named after Swedish logician Per Lindström, who published it in 1969) states that first-order logic is the strongest logic [1] (satisfying certain conditions, e.g. closure under classical negation) having both the (countable) compactness property and the (downward) Löwenheim–Skolem property. [2]
A formal proof of a well-formed formula in a proof system is a set of axioms and rules of inference of proof system that infers that the well-formed formula is a theorem of proof system. [ 2 ] Usually a given proof calculus encompasses more than a single particular formal system, since many proof calculi are under-determined and can be used for ...
Mathematical logic is the study of formal logic within mathematics. Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. Mathematical logic is divided into four parts: Model theory; Proof theory; Recursion theory, also known as computability theory ...