Related papers: Unification nets: canonical proof net quantifiers
A rather easy yet rigorous proof of a version of G\"odel's first incompleteness theorem is presented. The version is "each recursively enumerable theory of natural numbers with 0, 1, +, *, =, logical and, logical not, and the universal…
MLL proof equivalence is the problem of deciding whether two proofs in multiplicative linear logic are related by a series of inference permutations. It is also known as the word problem for star-autonomous categories. Previous work has…
First-order temporal logics are notorious for their bad computational behaviour. It is known that even the two-variable monadic fragment is highly undecidable over various linear timelines, and over branching time even one-variable…
Ill-founded (or non-wellfounded) proof systems have emerged as a natural framework for inductive and coinductive reasoning. In such systems, soundness relies on global correctness criteria, such as the progressivity condition. Ensuring that…
Herbrand's theorem is one of the most fundamental insights in logic. From the syntactic point of view it suggests a compact representation of proofs in classical first- and higher-order logic by recording the information which instances…
Machine reading comprehension with unanswerable questions is a new challenging task for natural language processing. A key subtask is to reliably predict whether the question is unanswerable. In this paper, we propose a unified model,…
Implementations of artificial neural networks (ANNs) might lead to failures, which are hardly predicted in the design phase since ANNs are highly parallel and their parameters are barely interpretable. Here, we develop and evaluate a novel…
In this paper, we introduce Linear Logic with a nondeterministic facility, which has a self-dual additive connective. In the system the proof net technology is available in a natural way. The important point is that nondeterminism in the…
Pure, or type-free, Linear Logic proof nets are Turing complete once cut-elimination is considered as computation. We introduce modal impredicativity as a new form of impredicativity causing the complexity of cut-elimination to be…
The cut-elimination procedure for the provability logic is known to be problematic: a L\"ob-like rule keeps cut-formulae intact on reduction, even in the principal case, thereby complicating the proof of termination. In this paper, we…
There is an increasing body of literature proposing new and efficient persistent versions of concurrent data structures ensuring that a consistent state can be recovered after a power failure or a crash. Their correctness is typically…
It is feasible and practically-valuable to bridge the characteristics between graph neural networks (GNNs) and logical reasoning. Despite considerable efforts and successes witnessed to solve Boolean satisfiability (SAT), it remains a…
Lipton's reduction theory provides an intuitive and simple way for deducing the non-interference properties of concurrent programs, but it is difficult to directly apply the technique to verify linearizability of sophisticated fine-grained…
Fair termination is the property of programs that may diverge "in principle" but that terminate "in practice", i.e. under suitable fairness assumptions concerning the resolution of non-deterministic choices. We study a conservative…
Linearizability is a commonly accepted notion of correctness for libraries of concurrent algorithms, and recent years have seen a number of proposals of program logics for proving it. Although these logics differ in technical details, they…
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…
The entanglement witness is an important and experimentally applicable tool for entanglement detection. In this paper, we provide a nonlinear improvement of any entanglement witness for $2\otimes d$ quantum systems. Compared with any…
Linear Logic was introduced by Girard as a resource-sensitive refinement of classical logic. It turned out that full propositional Linear Logic is undecidable (Lincoln, Mitchell, Scedrov, and Shankar) and, hence, it is more expressive than…
In response to the global challenge of mental health problems, we proposes a Logical Neural Network (LNN) based Neuro-Symbolic AI method for the diagnosis of mental disorders. Due to the lack of effective therapy coverage for mental…
We isolate a model-theoretic "standard-cut" phenomenon for true Pi0_1 sentences: if a model M satisfies ZFC + not-phi, then omega^M is not the standard omega, and any internal "witness" to not-phi is computationally inaccessible by…