Related papers: Subatomic Proof Systems: Splittable Systems
A cyclic proof system is a proof system whose proof figure is a tree with cycles. The cut-elimination in a proof system is fundamental. It is conjectured that the cut-elimination in the cyclic proof system for first-order logic with…
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…
Just as conventional functional programs may be understood as proofs in an intuitionistic logic, so quantum processes can also be viewed as proofs in a suitable logic. We describe such a logic, the logic of compact closed categories and…
Linear logical frameworks with subexponentials have been used for the specification of among other systems, proof systems, concurrent programming languages and linear authorization logics. In these frameworks, subexponentials can be…
Real-valued logics have seen a renewed interest in verification for probabilistic and quantitative systems, in particular machine learning models, where they can be used to directly integrate specifications in the training objective. To do…
Linear logic was conceived in 1987 by Girard and, in contrast to classical logic, restricts the usage of the structural inference rules of weakening and contraction. With this, atoms of the logic are no longer interpreted as truth, but as…
The integration of reasoning, learning, and decision-making is key to build more general artificial intelligence systems. As a step in this direction, we propose a novel neural-logic architecture, called differentiable logic machine (DLM),…
We extend the theoretical framework of proof mining by establishing general logical metatheorems that allow for the extraction of the computational content of theorems with prima facie "non-computational" proofs from probability theory,…
We revisit the results on admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables under several appropriate gauges of the arbitrary elements…
Probabilistic independence is a useful concept for describing the result of random sampling---a basic operation in all probabilistic languages---and for reasoning about groups of random variables. Nevertheless, existing verification methods…
Motivated by the quest for a logic for PTIME and recent insights that the descriptive complexity of problems from linear algebra is a crucial aspect of this problem, we study the solvability of linear equation systems over finite groups and…
We study orbit-finite systems of linear equations, in the setting of sets with atoms. Our principal contribution is a decision procedure for solvability of such systems. The procedure works for every field (and even commutative ring) under…
This paper builds model-theoretic tools to detect changes in complexity among the simple theories. We develop a generalization of dividing, called shearing, which depends on a so-called context c. This leads to defining c-superstability, a…
We introduce and study logic programs whose clauses are built out of monotone constraint atoms. We show that the operational concept of the one-step provability operator generalizes to programs with monotone constraint atoms, but the…
We provide the first (non-labelled) sequent calculi for bimodal provability logics with "usual" provability predicates. In particular, we introduce calculi for the logics CS, CSM and ER. Additionally, we present non-wellfounded versions of…
First-order logic has been established as an important tool for modeling and verifying intricate systems such as distributed protocols and concurrent systems. These systems are parametric in the number of nodes in the network or the number…
The Central Limit Theorem (CLT) establishes that sufficiently large sequences of independent and identically distributed random variables converge in probability to a normal distribution. This makes the CLT a fundamental building block of…
We characterise non-distributive positive logic as the fragment of a single-sorted first-order language that is preserved by a new notion of simulation called a meet-simulation. Meet-simulations distinguish themselves from simulations…
We study cut elimination for a multifocused variant of full linear logic in the sequent calculus. The multifocused normal form of proofs yields problems that do not appear in a standard focused system, related to the constraints in grouping…
In this paper we present a proof system that operates on graphs instead of formulas. Starting from the well-known relationship between formulas and cographs, we drop the cograph-conditions and look at arbitrary undirected) graphs. This…