Related papers: A Hoare logic for the coinductive trace-based big-…
We propose a simple imperative programming language, ERC, that features arbitrary real numbers as primitive data type, exactly. Equipped with a denotational semantics, ERC provides a formal programming language-theoretic foundation to the…
This draft introduces the technical machinery of a semantic framework for potentialist truthmaking based on our innovation of intentic states, which are structured partial models accounting for our distinction between non-hypothetical and…
Evaluating open-ended outputs from large language models (LLMs) remains challenging due to the absence of ground truth. Existing metrics rely on final-answer accuracy or surface-level statistics, leaving the reasoning process itself…
Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal…
This paper concerns the development of metatheory for extensible languages. It uses as its starting point a view that programming languages tailored to specific application domains are to be constructed by composing components from an open…
The purpose of this paper is to develop and study recursive proofs of coinductive predicates. Such recursive proofs allow one to discover proof goals in the construction of a proof of a coinductive predicate, while still allowing the use of…
The term {\em meta-programming} refers to the ability of writing programs that have other programs as data and exploit their semantics. The aim of this paper is presenting a methodology allowing us to perform a correct termination analysis…
Sound over-approximation methods have been proved effective for guaranteeing the absence of errors, but inevitably they produce false alarms that can hamper the programmers. Conversely, under-approximation methods are aimed at bug finding…
Large language models (LLMs) increasingly solve difficult problems by producing "reasoning traces" before emitting a final response. However, it remains unclear how accuracy and decision commitment evolve along a reasoning trajectory, and…
Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal…
We present a method for computing stable models of normal logic programs, i.e., logic programs extended with negation, in the presence of predicates with arbitrary terms. Such programs need not have a finite grounding, so traditional…
Using coalgebraic methods, we extend Conway's theory of games to possibly non-terminating, i.e. non-wellfounded games (hypergames). We take the view that a play which goes on forever is a draw, and hence rather than focussing on winning…
Many systems include components interacting with each other that evolve with possibly very different speeds. To deal with this situation many formal models adopt the abstraction of "zero-time transitions", which do not consume time. These…
Separation logic is used to reason locally about stateful programs. State of the art program logics for higher-order store are usually built on top of untyped operational semantics, in part because traditional denotational methods have…
We use modal logic as a framework for coalgebraic trace semantics, and show the flexibility of the approach with concrete examples such as the language semantics of weighted, alternating and tree automata, and the trace semantics of…
Specification languages are essential in deductive program verification, but they are usually based on first-order logic, hence less expressive than the programs they specify. Recently, trace specification logics with fixed points that are…
Left-sequential logics provide a means for reasoning about (closed) propositional terms with atomic propositions that may have side effects and that are evaluated sequentially from left to right. Such propositional terms are commonly used…
Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…
We see how nested sequents, a natural generalisation of hypersequents, allow us to develop a systematic proof theory for modal logics. As opposed to other prominent formalisms, such as the display calculus and labelled sequents, nested…
One recurring problem in program development is that of understanding how to re-use code developed by a third party. In the context of (constraint) logic programming, part of this problem reduces to figuring out how to query a program. If…