Related papers: Modular coinduction up-to for higher-order languag…
The bialgebraic abstract GSOS framework by Turi and Plotkin provides an elegant categorical approach to modelling the operational and denotational semantics of programming and process languages. In abstract GSOS, bisimilarity is always a…
The recently proposed CP language adopts Compositional Programming: a new modular programming style that solves challenging problems such as the Expression Problem. CP is implemented on top of a polymorphic core language with disjoint…
Cyber-Physical Systems (CPSs) are systems with both physical and software components, for example cars and industrial robots. Since these systems exhibit both discrete and continuous dynamics, they are complex and it is thus difficult to…
We study polymorphic type assignment systems for untyped lambda-calculi with effects, based on Moggi's monadic approach. Moving from the abstract definition of monads, we introduce a version of the call-by-value computational…
In order to combine operational and logical styles of specifications in one unified framework, the notion of logic labelled transition systems (Logic LTS, for short) has been presented and explored by L\"{u}ttgen and Vogler in [TCS…
Calculi with control operators have been studied as extensions of simple type theory. Real programming languages contain datatypes, so to really understand control operators, one should also include these in the calculus. As a first step in…
We propose a method that allows us to develop tableaux modulo theories using the principles of superdeduction, among which the theory is used to enrich the deduction system with new deduction rules. This method is presented in the framework…
Up-to techniques are a well-known method for enhancing coinductive proofs of behavioural equivalences. We introduce up-to techniques for behavioural metrics between systems modelled as coalgebras and we provide abstract results to prove…
The two Girard translations provide two different means of obtaining embeddings of Intuitionistic Logic into Linear Logic, corresponding to different lambda-calculus calling mechanisms. The translations, mapping A -> B respectively to !A -o…
Guarded recursion is a powerful modal approach to recursion that can be seen as an abstract form of step-indexing. It is currently used extensively in separation logic to model programming languages with advanced features by solving domain…
This paper proposes a modularized sense induction and representation learning model that jointly learns bilingual sense embeddings that align well in the vector space, where the cross-lingual signal in the English-Chinese parallel corpus is…
Satisfiability modulo theories (SMT) solvers have throughout the years been able to cope with increasingly expressive formulas, from ground logics to full first-order logic modulo theories. Nevertheless, higher-order logic within SMT is…
A recent research line has obtained strong results on bilingual lexicon induction by aligning independently trained word embeddings in two languages and using the resulting cross-lingual embeddings to induce word translation pairs through…
Large language models (LLMs) have become increasingly prevalent in our daily lives, leading to an expectation for LLMs to be trustworthy -- - both accurate and well-calibrated (the prediction confidence should align with its ground truth…
In this paper we consider first-order logic theorem proving and model building via approximation and instantiation. Given a clause set we propose its approximation into a simplified clause set where satisfiability is decidable. The…
Reasoning semantically in first-order logic is notoriously a challenge. This paper surveys a selection of semantically-guided or model-based methods that aim at meeting aspects of this challenge. For first-order logic we touch upon…
This paper introduces a simple and scalable approach to improve the data efficiency of large language model (LLM) training by augmenting existing text data with thinking trajectories. The compute for pre-training LLMs has been growing at an…
Representation theorems for formal systems often take the form of an inductive translation that satisfies certain invariants, which are proved inductively. Theory morphisms and logical relations are common patterns of such inductive…
Transitive closure logic is a known extension of first-order logic obtained by introducing a transitive closure operator. While other extensions of first-order logic with inductive definitions are a priori parametrized by a set of inductive…
Hierarchical transition systems provide a popular mathematical structure to represent state-based software applications in which different layers of abstraction are represented by inter-related state machines. The decomposition of high…