900 research outputs found
Correct Answers for First Order Logic
AbstractWorking within a semantic framework for sequent calculi developed in [3], we propose a couple of extensions to the concepts of correct answers and correct resultants which can be applied to the full first order logic. With respect to previous proposals, this is based on proof theory rather than model theory. We motivate our choice with several examples and we show how to use correct answers to reconstruct an abstraction which is widely used in the static analysis of logic programs, namely groundness. As an example of application, we present a prototypical top-down static interpreter for properties of groundness which works for the full intuitionistic first order logic
Primitive abundant and weird numbers with many prime factors
We give an algorithm to enumerate all primitive abundant numbers (briefly,
PANs) with a fixed (the number of prime factors counted with their
multiplicity), and explicitly find all PANs up to , count all PANs
and square-free PANs up to and count all odd PANs and odd
square-free PANs up to . We find primitive weird numbers (briefly,
PWNs) with up to 16 prime factors, improving the previous results of
[Amato-Hasler-Melfi-Parton] where PWNs with up to 6 prime factors have been
given. The largest PWN we find has 14712 digits: as far as we know, this is the
largest example existing, the previous one being 5328 digits long [Melfi]. We
find hundreds of PWNs with exactly one square odd prime factor: as far as we
know, only five were known before. We find all PWNs with at least one odd prime
factor with multiplicity greater than one and and prove that there
are none with . Regarding PWNs with a cubic (or higher) odd prime
factor, we prove that there are none with , and we did not find
any with larger . Finally, we find several PWNs with 2 square odd prime
factors, and one with 3 square odd prime factors. These are the first such
examples.Comment: New section on open problems. A mistake in table 2 corrected (# odd
PAN with Omega=8). New PWN in table 5, last line, 2 squared prime factors,
Omega=15. Updated bibliograph
Optimality in Goal-Dependent Analysis of Sharing
We face the problems of correctness, optimality and precision for the static
analysis of logic programs, using the theory of abstract interpretation. We
propose a framework with a denotational, goal-dependent semantics equipped with
two unification operators for forward unification (calling a procedure) and
backward unification (returning from a procedure). The latter is implemented
through a matching operation. Our proposal clarifies and unifies many different
frameworks and ideas on static analysis of logic programming in a single,
formal setting. On the abstract side, we focus on the domain Sharing by Jacobs
and Langen and provide the best correct approximation of all the primitive
semantic operators, namely, projection, renaming, forward and backward
unification. We show that the abstract unification operators are strictly more
precise than those in the literature defined over the same abstract domain. In
some cases, our operators are more precise than those developed for more
complex domains involving linearity and freeness.
To appear in Theory and Practice of Logic Programming (TPLP
The Abstract Domain of Parallelotopes
AbstractWe propose a numerical abstract domain based on parallelotopes. A parallelotope is a polyhedron whose constraint matrix is squared and invertible. The domain of parallelotopes is a fully relational abstraction of the Cousot and Halbwachsʼ polyhedra abstract domain, and does not use templates. We equip the domain of parallelotopes with all the necessary operations for the analysis of imperative programs, and show optimality results for the abstract operators
experimental evaluation of numerical domains for inferring ranges
Abstract Among the numerical abstract domains for detecting linear relationships between program variables, the polyhedra domain is, from a purely theoretical point of view, the most precise one. Other domains, such as intervals, octagons and parallelotopes, are less expressive but generally more efficient. We focus our attention on interval constraints and, using a suite of benchmarks, we experimentally show that, in practice, polyhedra may often compute results less precise than the other domains, due to the use of the widening operator
SAI, a Sensible Artificial Intelligence that plays Go
We propose a multiple-komi modification of the AlphaGo Zero/Leela Zero
paradigm. The winrate as a function of the komi is modeled with a
two-parameters sigmoid function, so that the neural network must predict just
one more variable to assess the winrate for all komi values. A second novel
feature is that training is based on self-play games that occasionally branch
-- with changed komi -- when the position is uneven. With this setting,
reinforcement learning is showed to work on 7x7 Go, obtaining very strong
playing agents. As a useful byproduct, the sigmoid parameters given by the
network allow to estimate the score difference on the board, and to evaluate
how much the game is decided.Comment: Updated for IJCNN 2019 conferenc
- …