Related papers: Unifying type systems for mobile processes
In this paper we explore the design of sequent calculi operating on graphs. For this purpose, we introduce a set of logical connectives allowing us to extend the correspondence between cographs and classical propositional formulas to any…
As businesses, products, and services spring up around large language models, the trustworthiness of these models hinges on the verifiability of their outputs. However, methods for explaining language model outputs largely fall across two…
Multiple types can represent the same concept. For example, lists and trees can both represent sets. Unfortunately, this easily leads to incomplete libraries: some set-operations may only be available on lists, others only on trees.…
Proof theory provides a foundation for studying and reasoning about programming languages, most directly based on the well-known Curry-Howard isomorphism between intuitionistic logic and the typed lambda-calculus. More recently, a…
Justification theory is a unifying framework for semantics of non-monotonic logics. It is built on the notion of a justification, which intuitively is a graph that explains the truth value of certain facts in a structure. Knowledge…
Display calculi are generalized sequent calculi which enjoy a `canonical' cut elimination strategy. That is, their cut elimination is uniformly obtained by verifying the assumptions of a meta-theorem, and is preserved by adding or removing…
We propose a novel approach for the formal verification of biological systems based on the use of a modal linear logic. We show how such a logic can be used, with worlds as instants of time, as an unified framework to encode both biological…
The paper gives a detailed presentation of a framework, embedded into the simply typed higher-order logic and aimed at the support of sound and structured reasoning about various properties of models of imperative programs with interleaved…
Type systems as a way to control or analyze programs have been largely studied in the context of functional programming languages. Some of those work allow to extract from a typing derivation for a program a complexity bound on this…
Session types statically prescribe bidirectional communication protocols for message-passing processes and are in a Curry-Howard correspondence with linear logic propositions. However, simple session types cannot specify properties beyond…
We introduce a formal meta-language for probabilistic programming, capable of expressing both programs and the type systems in which they are embedded. We are motivated here by the desire to allow an AGI to learn not only relevant knowledge…
Interprocedural flow analysis can be used to eliminate otherwise unnecessary heap allocated objects (unboxing), and in previous work we have shown how to do so while maintaining correctness with respect to the garbage collector. In this…
The increasing relevance of areas such as real-time and embedded systems, pervasive computing, hybrid systems control, and biological and social systems modeling is bringing a growing attention to the temporal aspects of computing, not only…
The design and analysis of systems that combine computational behaviour with physical processes' continuous dynamics - such as movement, velocity, and voltage - is a famous, challenging task. Several theoretical results from programming…
We define a fragment of propositional logic where isomorphic propositions, such as $A\land B$ and $B\land A$, or $A\Rightarrow (B\land C)$ and $(A\Rightarrow B)\land(A\Rightarrow C)$ are identified. We define System I, a proof language for…
Conceptual models as representations of real-world systems are based on diverse techniques in various disciplines but lack a framework that provides multidisciplinary ontological understanding of real-world phenomena. Concurrently, systems…
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…
In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…
In this chapter, we propose some future directions of work, potentially beneficial to Mathematics and its foundations, based on the recent import of methodology from the theory of programming languages into proof theory. This scientific…
Linear type systems need to keep track of how programs use their resources. The standard approach is to use context splits specifying how resources are (disjointly) split across subterms. In this approach, context splits redundantly echo…