Formal versus semiformal proof in teaching predicate logic

نویسندگان

  • David Gries
  • Steve Grantham
چکیده

This [kind of semiformal proof] is difficult to define precisely, but what I have in mind is the type of proof that most mathematicians would consider complete and rigorous, but that is not strictly formal in the sense of a purely syntactic derivation using a very precise and circumscribed formal set of rules of inference. In other words, I have in mind the type of proof found in a typical textbook on algebra, analysis, number theory, etc.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Deduction Chains for Logic of Common Knowledge

Deduction chains represent a syntactic and in a certain sense constructive method for proving completeness of a formal system S with respect to the class of S-structures. Given a formula A, the deduction chains of A are built up by systematically decomposing A into its subformulae. In the case where A is a valid formula, the decomposition yields a (usually cut-free) proof of A in the system S. ...

متن کامل

On Two Models of Provability

Gödel’s modal logic approach to analyzing provability attracted a great deal of attention and eventually led to two distinct mathematical models. The first is the modal logic GL, also known as the Provability Logic, which was shown in 1979 by Solovay to be the logic of the formal provability predicate. The second is Gödel’s original modal logic of provability S4, together with its explicit coun...

متن کامل

Automata Theory Approach to Predicate Intuitionistic Logic

Predicate intuitionistic logic is a well established fragment of dependent types. According to the Curry-Howard isomorphism proof construction in the logic corresponds well to synthesis of a program the type of which is a given formula. We present a model of automata that can handle proof construction in full intuitionistic first-order logic. The automata are constructed in such a way that any ...

متن کامل

A New Approach to Teaching Discrete Mathematics

We advocate teaching introductory discrete mathematics by first teaching equational propositional and predicate logic and then using it as tool (and not simply viewing it as an object of study) throughout the study of later topics —e.g. set theory, induction, relations, theory of integers, combinatorics, solving recurrence relations, and modern algebra. The in-depth (6–7 weeks) treatment of log...

متن کامل

A Teaching and Support Tool for Building Formal Models of Graphical User-Interfaces

In this paper we propose the design of a tool that will allow the construction of a formal, textual description of a software system even if it has a graphical user-interface as a component. An important aspect of this design is that it can be used for two purposes—the teaching of predicate calculus and the formal specification of graphical user-interfaces. The design has been suggested by cons...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1993