Concept
Complemented lattice
Related publications (37)
Interpolation and Quantifiers in Ortholattices
Viktor Kuncak, Simon Guilloud, Sankalp Gambhir
We study quantifiers and interpolation properties in ortho- logic, a non-distributive weakening of classical logic that is sound for formula validity with respect to classical logic, yet has a quadratic-time decision procedure. We present a sequent-based p ...
2024Interpolation and Quantifiers in Ortholattices
Viktor Kuncak, Simon Guilloud, Sankalp Gambhir
We study quantifiers and interpolation properties in orthologic, a non-distributive weakening of classical logic that is sound for formula validity with respect to classical logic, yet has a quadratic-time decision procedure. We present a sequent-based pro ...
Cham2024Orthologic with Axioms
We study the proof theory and algorithms for orthologic, a logical system based on ortholattices, which have shown practical relevance in simplification and normalization of verification conditions. Ortholattices weaken Boolean algebras while having po ...
Mean value theorems for collections of lattices with a prescribed group of symmetries
Euclidean lattices are mathematical objects of increasing interest in the fields of cryptography and error-correcting codes. This doctoral thesis is a study on high-dimensional lattices with the motivation to understand how efficient they are in terms of b ...
EPFL2024Moments of the number of points in a bounded set for number field lattices
Maryna Viazovska, Nihar Prakash Gargava, Vlad Serban
We examine the moments of the number of lattice points in a fixed ball of volume for lattices in Euclidean space which are modules over the ring of integers of a number field . In particular, denoting by the number of roots of unity in , we ...
arXiv2023LISA – A Modern Proof System
Viktor Kuncak, Simon Guilloud, Sankalp Gambhir
We present LISA, a proof system and proof assistant for constructing proofs in schematic first-order logic and axiomatic set theory. The logical kernel of the system is a proof checker for first-order logic with equality and schematic predicate and fun ...
2023On Polynomial Algorithms for Normalizing Formulas
Viktor Kuncak, Simon Guilloud, Mario Bucev
We propose a new approach for normalization and simplification of logical formulas. Our approach is based on algorithms for lattice-like structures. Specifically, we present two efficient algorithms for computing a normal form and deciding the word problem ...
2022Packing the Boolean lattice with copies of a poset
The Boolean lattice (2[n],subset of) is the family of all subsets of [n]={1,MIDLINE HORIZONTAL ELLIPSIS,n}, ordered by inclusion. Let P be a partially ordered set. We prove that if n is sufficiently large, then there exists a packing P of copies of P in (2 ...
WILEY2020New Results in Integer and Lattice Programming
An integer program (IP) is a problem of the form , where , , , and is a separable convex objective function.
The problem o ...
EPFL2020