Related papers: Proof Nets for PiL (Full Version)
Class incremental learning (CIL) algorithms aim to continually learn new object classes from incrementally arriving data while not forgetting past learned classes. The common evaluation protocol for CIL algorithms is to measure the average…
Mixed integer linear programming (MILP) is a powerful representation often used to formulate decision-making problems under uncertainty. However, it lacks a natural mechanism to reason about objects, classes of objects, and relations.…
By adapting Salomaa's complete proof system for equality of regular expressions under the language semantics, Milner (1984) formulated a sound proof system for bisimilarity of regular expressions under the process interpretation he…
Uniform proofs are sequent calculus proofs with the following characteristic: the last step in the derivation of a complex formula at any stage in the proof is always the introduction of the top-level logical symbol of that formula. We…
Full Intuitionistic Linear Logic (FILL) is multiplicative intuitionistic linear logic extended with par. Its proof theory has been notoriously difficult to get right, and existing sequent calculi all involve inference rules with complex…
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…
We provide here a proof theoretic account of constraint programming that attempts to capture the essential ingredients of this programming style. We exemplify it by presenting proof rules for linear constraints over interval domains, and…
Several variants of linear logic have been proposed to characterize complexity classes in the proofs-as-programs correspondence. Light linear logic (LLL) ensures a polynomial bound on reduction time, and characterizes in this way polynomial…
We define a strongly normalising proof-net calculus corresponding to the logic of strongly compact closed categories with biproducts. The calculus is a full and faithful representation of the free strongly compact closed category with…
Petri nets are a well-known model of concurrency and provide an ideal setting for the study of fundamental aspects in concurrent systems. Despite their simplicity, they still lack a satisfactory causally reversible semantics. We develop…
We present $\mathcal{MEL}^{++}$ (M denotes Markov logic networks) an extension of the log-linear description logics $\mathcal{EL}^{++}$-LL with concrete domains, nominals, and instances. We use Markov logic networks (MLNs) in order to find…
A logic calculus is presented that is a conservative extension of linear logic. The motivation beneath this work concerns lazy evaluation, true concurrency and interferences in proof search. The calculus includes two new connectives to deal…
We define and study translations between the maximal class of analytic display calculi for tense logics and labeled sequent calculi, thus solving an open problem about the translatability of proofs between the two formalisms. In particular,…
We give a new characterization of elementary and deterministic polynomial time computation in linear logic through the proofs-as-programs correspondence. Girard's seminal results, concerning elementary and light linear logic, achieve this…
A key feature of inductive logic programming (ILP) is its ability to learn first-order programs, which are intrinsically more expressive than propositional programs. In this paper, we introduce techniques to learn higher-order programs.…
The formalism of the models with Petri networks provides a sound theoretical base, supported by powerful mathematical methods able to extract information necessary for the formalism and simulation of the real system that provides features…
This notes explains how standard algorithms that construct sorting networks have been formalised and proved correct in the Coq proof assistant using the SSReflect extension.
Equational reasoning with string diagrams provides an intuitive means of proving equations between morphisms in a symmetric monoidal category. This can be extended to proofs of infinite families of equations using a simple graphical syntax…
Permissive-Nominal Logic (PNL) is an extension of first-order predicate logic in which term-formers can bind names in their arguments. This allows for direct axiomatisations with binders, such as of the lambda-binder of the lambda-calculus…
The overall goal of this paper is to investigate the theoretical foundations of algorithmic verification techniques for first order linear logic specifications. The fragment of linear logic we consider in this paper is based on the linear…