Related papers: Complete Dynamic Logic of Communicating Hybrid Pro…
Definition packages in theorem provers provide users with means of defining and organizing concepts of interest. This system description presents a new definition package for the hybrid systems theorem prover KeYmaera X based on…
In relational verification, judicious alignment of computational steps facilitates proof of relations between programs using simple relational assertions. Relational Hoare logics (RHL) provide compositional rules that embody various…
Dynamical systems are abstract models of interaction between space and time. They are often used in fields such as physics and engineering to understand complex processes, but due to their general nature, they have found applications for…
Transition systems are often used to describe the behaviour of software systems. If viewed as a graph then, at their most basic level, vertices correspond to the states of a program and each edge represents a transition between states via…
The complexity of modern software systems entails the need for reconfiguration mechanisms gov- erning the dynamic evolution of their execution configurations in response to both external stimulus or internal performance measures. Formally,…
Despite recent advancements in large language models (LLMs), their performance on complex reasoning problems requiring multi-step thinking and combining various skills is still limited. To address this, we propose a novel framework HDFlow…
Building on our previous work on hybrid polyadic modal logic we identify modal logic equivalents for Matching Logic, a logic for program specification and verification. This provides a rigorous way to transfer results between the two…
The field of Distributed Constraint Optimization Problems (DCOPs) has gained momentum, thanks to its suitability in capturing complex problems (e.g., multi-agent coordination and resource allocation problems) that are naturally distributed…
We investigate the automatic differentiation of hybrid models, viz. models that may contain delays, logical tests and discontinuities or loops. We consider differentiation with respect to parameters, initial conditions or the time. We…
Multi-core and highly-connected architectures have become ubiquitous, and this has brought renewed interest in language-based approaches to the exploitation of parallelism. Since its inception, logic programming has been recognized as a…
We propose a new version of generalized probabilistic propositional logic, namely, discrete-continuous logic (DCL) in which every generalized proposition (GP) is represented as 2x2 nondiagonal positive matrix with unit trace. We demonstrate…
Process calculi based on logic, such as $\pi$DILL and CP, provide a foundation for deadlock-free concurrent programming. However, in previous work, there is a mismatch between the rules for constructing proofs and the term constructors of…
Synchronous model is a type of formal models for modelling and specifying reactive systems. It has a great advantage over other real-time models that its modelling paradigm supports a deterministic concurrent behaviour of systems. Various…
This thesis focuses on advancing probabilistic logic programming (PLP), which combines probability theory for uncertainty and logic programming for relations. The thesis aims to extend PLP to support both discrete and continuous random…
Logic Programs with Ordered Disjunction (LPODs) extend classical logic programs with the capability of expressing preferential disjunctions in the heads of program rules. The initial semantics of LPODs, although simple and quite intuitive,…
Labelled tableaux have been a traditional approach to define satisfiability checking procedures for Modal Logics. In many cases, they can also be used to obtain tight complexity bounds and lead to efficient implementations of reasoning…
Multi-hop reasoning for question answering (QA) plays a critical role in retrieval-augmented generation (RAG) for modern large language models (LLMs). The accurate answer can be obtained through retrieving relational structure of entities…
The main contribution of the present paper is the introduction of a simple yet expressive hybrid-dynamic logic for describing quantum programs. This version of quantum logic can express quantum measurements and unitary evolutions of states…
Chain-of-Thought (CoT) reasoning significantly elevates the complex problem-solving capabilities of multimodal large language models (MLLMs). However, adapting CoT to vision typically discretizes signals to fit LLM inputs, causing early…
Programmable Logic Controllers (PLCs) provide a prominent choice of implementation platform for safety-critical industrial control systems. Formal verification provides ways of establishing correctness guarantees, which can be quite…