Related papers: Higher-Order Behavioural Conformances via Fibratio…
While distributed systems with transfer of processes have become pervasive, methods for reasoning about their behaviour are underdeveloped. In this paper we propose a bisimulation technique for proving behavioural equivalence of such…
Previous results on proving confluence for Constraint Handling Rules are extended in two ways in order to allow a larger and more realistic class of CHR programs to be considered confluent. Firstly, we introduce the relaxed notion of…
Type soundness is an important property of modern programming languages. In this paper we explore the idea that "well-typed languages are sound": the idea that the appropriate typing discipline over language specifications guarantees that…
Coinduction occurs in two guises in Horn clause logic: in proofs of self-referencing properties and relations, and in proofs involving construction of (possibly irregular) infinite data. Both instances of coinductive reasoning appeared in…
Reasoning is a fundamental capability of Large Language Models. While prior research predominantly focuses on enhancing narrow skills like math or code generation, improving performance on many other reasoning tasks remains challenging due…
The logic programming paradigm provides the basis for a new intensional view of higher-order notions. This view is realized primarily by employing the terms of a typed lambda calculus as representational devices and by using a richer form…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
We aim to create the highest possible quality of treatment-control matches for categorical data in the potential outcomes framework. Matching methods are heavily used in the social sciences due to their interpretability, but most matching…
We describe an approach to the verified implementation of transformations on functional programs that exploits the higher-order representation of syntax. In this approach, transformations are specified using the logic of hereditary Harrop…
A variety of logical frameworks support the use of higher-order abstract syntax (HOAS) in representing formal systems. Although these systems seem superficially the same, they differ in a variety of ways; for example, how they handle a…
We propose to study proof search from a coinductive point of view. In this paper, we consider intuitionistic logic and a focused system based on Herbelin's LJT for the implicational fragment. We introduce a variant of lambda calculus with…
Deductive verification techniques based on program logics (i.e., the family of Floyd-Hoare logics) are a powerful approach for program reasoning. Recently, there has been a trend of increasing the expressive power of such logics by…
Abductive logic programming offers a formalism to declaratively express and solve problems in areas such as diagnosis, planning, belief revision and hypothetical reasoning. Tabled logic programming offers a computational mechanism that…
Like notions of process equivalence, behavioural preorders on processes come in many flavours, ranging from fine-grained comparisons such as ready simulation to coarse-grained ones such as trace inclusion. Often, such behavioural preorders…
Requirement traceability is the process of identifying the inter-dependencies between requirements. It poses a significant challenge when conducted manually, especially when dealing with requirements at various levels of abstraction. In…
This paper presents matching logic, a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives…
Probabilistic programming provides a convenient lingua franca for writing succinct and rigorous descriptions of probabilistic models and inference tasks. Several probabilistic programming languages, including Anglican, Church or Hakaru,…
We introduce languages of higher-dimensional automata (HDAs) and develop some of their properties. To this end, we define a new category of precubical sets, uniquely naturally isomorphic to the standard one, and introduce a notion of event…
Chain-of-thought (CoT) reasoning with self-consistency improves performance by aggregating multiple sampled reasoning paths. In this setting, correctness is no longer tied to a single reasoning trace but to the aggregation rule over a pool…
Compositionality proofs in higher-order languages are notoriously involved, and general semantic frameworks guaranteeing compositionality are hard to come by. In particular, Turi and Plotkin's bialgebraic abstract GSOS framework, which…