Enumerating Proofs of Positive Formulae
نویسندگان
چکیده
We provide a semi-grammatical description of the set of normal proofs of positive formulae in minimal predicate logic, i.e. a grammar that generates a set of schemes, from each of which we can produce a finite number of normal proofs. This method is complete in the sense that each normal proof-term of the formula is produced by some scheme generated by the grammar. As a corollary, we get a similar description of the set of normal proofs of positive formulae for a large class of theories including simple type theory and System F.
منابع مشابه
Automatic Proofs for Formulae Enumerating Proper Polycubes
We develop a general framework for computing formulae enumerating polycubes of size n which are proper in n−k dimensions (spanning all n−k dimensions), for a fixed value of k. Besides the fundamental importance of knowing the number of these simple combinatorial objects, such formulae are central in the literature of statistical physics in the study of percolation processes and the collapse of ...
متن کاملOn the enumeration of partitions with summands in arithmetic progression
Enumerating formulae are constructed which count the number of partitions of a positive integer into positive summands in arithmetic progression with common difference D. These enumerating formulae (denoted pD(n)) which are given in terms of elementary divisor functions together with auxiliary arithmetic functions (to be defined) are then used to establish a known characterisation for an intege...
متن کاملA Proof-Theoretic Analysis of Goal-Directed Provability
Uniform proofs have been presented as a basis for logic programming, and it is known that by restricting the class of formulae it is possible to guarantee that uniform proofs are complete with respect to provability in intuitionistic logic. In this paper we explore the relationship between uniform proofs and classes of formulae more deeply. Firstly we show that uniform proofs arise naturally as...
متن کاملIntuitive Counterexamples for Constructive Fallacies
Formal countermodels may be used to justify the unprovability of formulae in the Heyting calculus (the best accepted formal system for constructive reasoning), on the grounds that unprovable formulae are constructively invalid. We argue that the intuitive impact of such countermodels becomes more transparent and convincing as we move from Kripke/Beth models based on possible worlds, to Läuchli ...
متن کاملFibre products of supersingular curves and the enumeration of irreducible polynomials with prescribed coefficients
For any positive integers n ≥ 3, r ≥ 1 we present formulae for the number of irreducible polynomials of degree n over the finite field F2r where the coefficients of xn−1, xn−2 and xn−3 are zero. Our proofs involve counting the number of points on certain algebraic curves over finite fields, a technique which arose from Fourier-analysing the known formulae for the F2 base field cases, reverse-en...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Comput. J.
دوره 52 شماره
صفحات -
تاریخ انتشار 2009