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We continue our investigation into hybrid polyadic multi-sorted logic with a focus on expresivity related to the operational and axiomatic semantics of rogramming languages, and relations with first-order logic. We identify a fragment of…

The performance of large language models (LLMs) and large multimodal models (LMMs) depends heavily on the quality and scale of their pre-training datasets. Recent research shows that large multimodal models trained on natural documents…

Concurrent separation logic with fractional permissions (CSLPerm) provides a promising reasoning system to verify most complex sequential and concurrent fine-grained programs. The logic with strong and weak separating conjunctions offers a…

Type-based amortised resource analysis following Hofmann and Jost---where resources are associated with individual elements of data structures and doled out to the programmer under a linear typing discipline---have been successful in…

First-Order Logic (FOL) is widely regarded as one of the most important foundations for knowledge representation. Nevertheless, in this paper, we argue that FOL has several critical issues for this purpose. Instead, we propose an…

As the expansion of IoT connectivity continues to provide quality-of-life improvements around the world, they simultaneously introduce increasing privacy and security concerns. The lack of a clear definition in managing shared and protected…

Separation logic is a Hoare-style logic for reasoning about programs with heap-allocated mutable data structures. As a step toward extending separation logic to high-level languages with ML-style general (higher-order) storage, we…

Logic programming provides a very high-level view of programming, which comes at the cost of some execution efficiency. Improving performance of logic programs is thus one of the holy grails of Prolog system implementations and a wide range…

We present a logical separability analysis for a functional quantum computation language. This logic is inspired by previous works on logical analysis of aliasing for imperative functional programs. Both analyses share similarities notably…

Logical reasoning about program data often requires dealing with heap structures as well as scalar data types. Recent advances in Satisfiability Modular Theory (SMT) already offer efficient procedures for dealing with scalars, yet they lack…

WebAssembly (Wasm) has risen as a widely used technology to distribute computing workloads on different platforms. The platform independence offered through Wasm makes it an attractive solution for many different applications that can run…

Formal verification provides strong guarantees of correctness of software, which are especially important in safety or security critical systems. Hoare logic is a widely used formalism for rigorous verification of software against…

We present the first formalization and metatheory of language soundness for a user-schedulable language, the widely used array processing language Halide. User-schedulable languages strike a balance between abstraction and control in…

In modern software development, the JavaScript ecosystem of various frameworks and libraries used to develop contemporary web applications presents many advantages. JavaScript is a widely known interpreted programming language, simple to…

We present an implementation of a probabilistic first-order logic called TensorLog, in which classes of logical queries are compiled into differentiable functions in a neural-network infrastructure such as Tensorflow or Theano. This leads…

Artificial Intelligence aims to provide computer programs with commonsense knowledge to reason about our world. This paper offers a new practical approach towards automated commonsense reasoning with first-order logic (FOL) ontologies. We…

Logic programming languages present clear advantages in terms of declarativeness and conciseness. However, the ideas of logic programming have been met with resistance in other programming communities, and have not generally been adopted by…

Orchestrating centralised service-oriented workflows presents significant scalability challenges that include: the consumption of network bandwidth, degradation of performance, and single points of failure. This paper presents a high-level…

Formal ontologies are axiomatizations in a logic-based formalism. The development of formal ontologies, and their important role in the Semantic Web area, is generating considerable research on the use of automated reasoning techniques and…

Satisfiability-based automated reasoning is an approach that is being successfully used in software engineering to validate complex software, including for safety-critical systems. Such reasoning underlies many validation activities, from…