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This paper combines the classical model of labeled transition systems with the epistemic model for reasoning about knowledge. The result is a unifying framework for modeling and analyzing multi-agent, knowledge-based, dynamic systems. On…
We present a method for synthesizing recursive functions that provably satisfy a given specification in the form of a polymorphic refinement type. We observe that such specifications are particularly suitable for program synthesis for two…
This article exhibits a particular encoding of logic circuits into a sheaf formalism. The central result of this article is that there exists strictly more information available to a circuit designer in this setting than exists in static…
In this article, we study parameterized complexity theory from the perspective of logic, or more specifically, descriptive complexity theory. We propose to consider parameterized model-checking problems for various fragments of first-order…
Parametricity is a key metatheoretic property of type systems, which implies strong uniformity & modularity properties of the structure of types within systems possessing it. In recent years, various systems of dependent type theory have…
We study the expressive power of the LARA language -- a recently proposed unified model for expressing relational and linear algebra operations -- both in terms of traditional database query languages and some analytic tasks often performed…
This paper updates the cognitive model, firstly by creating two systems and then unifying them over the same structure. It represents information at the semantic level only, where labelled patterns are aggregated into a 'type-set-match'…
A theory graph is a network of axiomatic theories connected with meaning-preserving mappings called theory morphisms. Theory graphs are well suited for organizing large bodies of mathematical knowledge. Traditional and formal proofs do not…
LF has been designed and successfully used as a meta-logical framework to represent and reason about object logics. Here we design a representation of the Isabelle logical framework in LF using the recently introduced module system for LF.…
This paper relates the well-known Linear Temporal Logic with the logic of propositional schemata introduced by the authors. We prove that LTL is equivalent to a class of schemata in the sense that polynomial-time reductions exist from one…
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…
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…
We present a simple and concise semantics for temporal planning. Our semantics are developed and formalised in the logic of the interactive theorem prover Isabelle/HOL. We derive from those semantics a validation algorithm for temporal…
Belief systems are often treated as globally consistent sets of propositions or as scalar-valued probability distributions. Such representations tend to obscure the internal structure of belief, conflate external credibility with internal…
Applying dynamic logics to program verifications is a challenge, because their axiomatic rules for regular expressions can be difficult to be adapted to different program models. We present a novel dynamic logic, called DLp, which supports…
Formal verification via theorem proving enables the expressive specification and rigorous proof of software correctness, but it is difficult to scale due to the significant manual effort and expertise required. While Large Language Models…
Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In…
This paper discusses the formalization of proofs "by diagram chasing", a standard technique for proving properties in abelian categories. We discuss how the essence of diagram chases can be captured by a simple many-sorted first-order…
Open-textured terms in written rules are typically settled through interpretive argumentation. Ongoing work has attempted to catalogue the schemes used in such interpretive argumentation. But how can the use of these schemes affect the way…
Craig's interpolation theorem (Craig 1957) is an important theorem known for propositional logic and first-order logic. It says that if a logical formula $\beta$ logically follows from a formula $\alpha$, then there is a formula $\gamma$,…