Related papers: A cyclic proof system for Guarded Kleene Algebra w…

One challenge in fact checking is the ability to improve the transparency of the decision. We present a fact checking method that uses reference information in knowledge graphs (KGs) to assess claims and explain its decisions. KGs contain a…

Answering complex queries over incomplete knowledge graphs (KGs) is a challenging job. Most previous works have focused on learning entity/relation embeddings and simulating first-order logic operators with various neural networks. However,…

We prove two completeness results for Kleene algebra with tests and a top element, with respect to guarded string languages and binary relations. While the equational theories of those two classes of models coincide over the signature of…

This paper presents McNetKAT, a scalable tool for verifying probabilistic network programs. McNetKAT is based on a new semantics for the guarded and history-free fragment of Probabilistic NetKAT in terms of finite-state, absorbing Markov…

Concurrent Kleene Algebra (CKA) is a recently proposed algebraic structure by Hoare and collaborators that unifies the laws of concurrent programming. The unifying power of CKA rests largely on the so-called exchange law that describes how…

This article describes a formal strategy of geometric complexity theory (GCT) to resolve the {\em self referential paradox} in the $P$ vs. $NP$ and related problems. The strategy, called the {\em flip}, is to go for {\em explicit proofs} of…

A cyclic proof system allows us to perform inductive reasoning without explicit inductions. We propose a cyclic proof system for HFLN, which is a higher-order predicate logic with natural numbers and alternating fixed-points. Ours is the…

We present MatchKAT, an algebraic language for modeling match-action packet processing in network switches. Although the match-action paradigm has remained a popular low-level programming model for specifying packet forwarding behavior,…

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…

Lambek calculus is a logical foundation of categorial grammar, a linguistic paradigm of grammar as logic and parsing as deduction. Pentus (2010) gave a polynomial-time algorithm for determ- ining provability of bounded depth formulas in the…

This research started with an algebra for reasoning about rely/guarantee concurrency for a shared memory model. The approach taken led to a more abstract algebra of atomic steps, in which atomic steps synchronise (rather than interleave)…

Cyclic proof theory studies proofs where cycles are allowed. This is useful for developing proof theory for logics with fixpoint operators: cycles can be used to represent the unfolding of a fixpoint. However, this cyclic character is not…

We study Hoare-like logics, including partial and total correctness Hoare logic, incorrectness logic, Lisbon logic, and many others through the lens of predicate transformers \`a la Dijkstra and through the lens of Kleene algebra with top…

We propose a new cyclic proof system for automated, equational reasoning about the behaviour of pure functional programs. The key to the system is the way in which cyclic proof and equational reasoning are mediated by the use of contextual…

Learning-based systems are increasingly deployed across various domains, yet the complexity of traditional neural networks poses significant challenges for formal verification. Unlike conventional neural networks, learned Logic Gate…

We consider cyclic proof systems in which derivations are graphs rather than trees. Such systems typically come with a condition that isolates which derivations are admitted as 'proofs', known as a the soundness condition. This soundness…

Existing Computerized Adaptive Testing (CAT) frameworks typically select questions based on the predicted likelihood that the student will answer correctly. This design ignores information contained in students' open-ended responses,…

We aim at a holistic perspective on program logics, including Hoare and incorrectness logics. To this end, we study different classes of properties arising from the generalization of the aforementioned logics. We compare our results with…

Concurrent Kleene Algebra (CKA) is a formalism to study concurrent programs. Like previous Kleene Algebra extensions, developing a correspondence between denotational and operational perspectives is important, for both foundations and…

This paper introduces a comprehensive framework for the evaluation and validation of generative language models (GLMs), with a focus on Retrieval-Augmented Generation (RAG) systems deployed in high-stakes domains such as banking. GLM…