Related papers: Logical metatheorems for accretive and (generalize…
This paper concerns three classes of real-valued functions on intervals, operator monotone functions, operator convex functions, and strongly operator convex functions. Strongly operator convex functions were previously treated in [3] and…
Notions of computation can be modelled by monads. Algebraic effects offer a characterization of monads in terms of algebraic operations and equational axioms, where operations are basic programming features, such as reading or updating the…
This paper develops a proof-theoretic framework for abstract interpretation by systematically associating logical systems with finite abstractions. Building on earlier work on the internal logics of abstractions, we propose a general…
Operads are algebraic devices offering a formalization of the concept of operations with several inputs and one output. Such operations can be naturally composed to form bigger and more complex ones. Coming historically from algebraic…
Cumulative logics are studied in an abstract setting, i.e., without connectives, very much in the spirit of Makinson's early work. A powerful representation theorem characterizes those logics by choice functions that satisfy a weakening of…
Kohlenbach's proof mining program deals with the extraction of effective information from typically ineffective proofs. Proof mining has its roots in Kreisel's pioneering work on the so-called unwinding of proofs. The proof mining of…
Computability logic is a formal theory of computational tasks and resources. Its formulas represent interactive computational problems, logical operators stand for operations on computational problems, and validity of a formula is…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
In this paper, we give precise mathematical form to the idea of a structure whose data and axioms are faithfully represented by a graphical calculus; some prominent examples are operads, polycategories, properads, and PROPs. Building on the…
In the logic programming paradigm, a program is defined by a set of methods, each of which can be executed when specific conditions are met during the current state of an execution. The semantics of these programs can be elegantly…
Argument mining is natural language processing technology aimed at identifying arguments in text. Furthermore, the approach is being developed to identify the premises and claims of those arguments, and to identify the relationships between…
Interest in anti-unification, the dual problem of unification, is on the rise due to applications within the field of software analysis and related areas. For example, anti-unification-based techniques have found uses within clone detection…
Non-normal modal logics, interpreted on neighbourhood models which generalise the usual relational semantics, have found application in several areas, such as epistemic, deontic, and coalitional reasoning. We present here preliminary…
We develop a general theory of operator realizations, or ``linear representations" of analytic functions in several non-commuting variables about a matrix-centre. In particular we show that a non-commutative function has a matrix-centre…
Linear Logic refines Intuitionnistic Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various frameworks. The most famous are indexed linear logics which…
The standard approach to logic in the literature in philosophy and mathematics, which has also been adopted in computer science, is to define a language (the syntax), an appropriate class of models together with an interpretation of…
Generally-unbounded infinitesimal generators are studied in the context of operator topology. Beginning with the definition of seminorm, the concept of locally convex topological vector space is introduced as well as the concept of…
While model checking has often been considered as a practical alternative to building formal proofs, we argue here that the theory of sequent calculus proofs can be used to provide an appealing foundation for model checking. Since the…
The probabilistic satisfiability of a logical expression is a fundamental concept known as the partition function in statistical physics and field theory, an evaluation of a related graph's Tutte polynomial in mathematics, and the…
We construct a resource theory of sharpness for finite-dimensional positive operator-valued measures (POVMs), where the sharpness-non-increasing operations are given by quantum preprocessing channels and convex mixtures with POVMs whose…