Related papers: Linear Logic by Levels and Bounded Time Complexity
The logic of definitions is a family of logics for encoding and reasoning about judgments, which are atomic predicates specified by inference rules. A definition associates an atomic predicate with a logical formula, which may itself depend…
We introduce LAM, a subsystem of IMALL2 with restricted additive rules able to manage duplication linearly, called linear additive rules. LAM is presented as the type assignment system for a calculus endowed with copy constructors, which…
We show that context semantics can be fruitfully applied to the quantitative analysis of proof normalization in linear logic. In particular, context semantics lets us define the weight of a proof-net as a measure of its inherent complexity:…
Ordered, linear, and other substructural type systems allow us to expose deep properties of programs at the syntactic level of types. In this paper, we develop a family of unary logical relations that allow us to prove consequences of…
Deep learning is very effective at jointly learning feature representations and classification models, especially when dealing with high dimensional input patterns. Probabilistic logic reasoning, on the other hand, is capable to take…
In Linear Logic ($\mathsf{LL}$), the exponential modality $!$ brings forth a distinction between non-linear proofs and linear proofs, where linear means using an argument exactly once. Differential Linear Logic ($\mathsf{DiLL}$) is an…
We confront two integrability criteria for rational mappings. The first is the singularity confinement based on the requirement that every singularity, spontaneously appearing during the iteration of a mapping, disappear after some steps.…
The ramification method in Implicit Computational Complexity has been associated with functional programming, but adapting it to generic imperative programming is highly desirable, given the wider algorithmic applicability of imperative…
The logic programming paradigm provides the basis for a new intensional view of higher-order notions. This view is realized primarily by employing the terms of a typed lambda calculus as representational devices and by using a richer form…
In this paper, we present a typed lambda calculus ${\bf SILL}(\lambda)_{\Sigma}$, a type-theoretic version of intuitionistic linear logic with subexponentials, that is, we have many resource comonadic modalities with some interconnections…
We describe a type system for the linear-algebraic lambda-calculus. The type system accounts for the part of the language emulating linear operators and vectors, i.e. it is able to statically describe the linear combinations of terms…
A distributed logic programming language with support for meta-programming and stream processing offers a variety of interesting research problems, such as: How can a versatile and stable data structure for the indexing of a large number of…
We identify a common scheme in several existing algorithms addressing computational problems on linear differential equations with polynomial coefficients. These algorithms reduce to computing a linear relation between vectors obtained as…
Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we…
Linear typed $\lambda$-calculi are more delicate than their simply typed siblings when it comes to metatheoretic results like preservation of typing under renaming and substitution. Tracking the usage of variables in contexts places more…
This paper presents a many-sorted polyadic modal logic that generalizes some of the existing approaches. The algebraic semantics has led us to a many-sorted generalization of boolean algebras with operators, for which we prove the analogue…
Type systems which account for resource sensitive computations can generally be split into two styles: First, substructural logics such as Linear Logic which seek to restrict weakening and contraction and reintroduce them in a controlled…
The emphasis is made on the juxtaposition of (quantum~theorem) proving versus quantum (theorem~proving). The logical contents of verification of the statements concerning quantum systems is outlined. The Zittereingang (trembling input)…
The differentiable implementation of logic yields a seamless combination of symbolic reasoning and deep neural networks. Recent research, which has developed a differentiable framework to learn logic programs from examples, can even acquire…
Computational interpretations of linear logic allow static control of memory resources: the data produced by the program are endowed through its type with attributes that determine its life cycle, and guarantee safe deallocation. The use of…