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Orthologic with Axioms

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Interpolation 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 ...

Cham2024

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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 ...

2024

SC-TPTP: An Extension of the TPTP Derivation Format for Sequent-Based Calculus

Simon Guilloud

Motivated by the transfer of proofs between proof systems, and in particular from first order automated theorem provers (ATPs) to interactive theorem provers (ITPs), we specify an extension of the TPTP derivation text format to describe proofs in first-ord ...

2024

LISA – 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 ...

2023

, ,

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 ...

2022

A Toolbox for Barriers on Interactive Oracle Proofs

Alessandro Chiesa

Interactive oracle proofs (IOPs) are a proof system model that combines features of interactive proofs (IPs) and probabilistically checkable proofs (PCPs). IOPs have prominent applications in complexity theory and cryptography, most notably to constructing ...

SPRINGER INTERNATIONAL PUBLISHING AG2022

On the Power and Limitations of Branch and Cut

Mika Tapani Göös

The Stabbing Planes proof system [Paul Beame et al., 2018] was introduced to model the reasoning carried out in practical mixed integer programming solvers. As a proof system, it is powerful enough to simulate Cutting Planes and to refute the Tseitin formu ...

Schloss Dagstuhl - Leibniz-Zentrum für Informatik2021

A comment on performance guarantees of a greedy algorithm for minimizing a supermodular set function on comatroid

Maryam Kamgarpour, Baiwei Guo, Orcun Karaca

We provide a counterexample to the performance guarantee obtained in the paper "Il'ev, V., Linker, N., 2006. Performance guarantees of a greedy algorithm for minimizing a supermodular set function on comatroid", which was published in Volume 171 of the Eur ...

ELSEVIER2021

Structural Rewriting in XOR-Majority Graphs

Giovanni De Micheli, Mathias Soeken, Zhufei Chu

In this paper, we present a structural rewriting method for a recently proposed XOR-Majority graph (XMG), which has exclusive-OR (XOR), majority-of-three (MAJ), and inverters as primitives. XMGs are an extension of Majority-Inverter Graphs (MIGs). Previous ...

ASSOC COMPUTING MACHINERY2019

Design and Evaluation of a Bowden-Cable-Based Remote Actuation System for Wearable Robotics

Roger Gassert, Olivier Lambercy

Wearable robots can assist motor-impaired individuals in activities of daily living, but weight is paramount for usability. Proximally placed actuators and remote actuation systems (RAS) minimize weight on users' extremities. State-of-the-art RAS employ pn ...

2018