Related papers: An Equational Theory for Weak Bisimulation via Gen…
Parameterized systems play a crucial role in the computer field, and their security is of great significance. Formal verification of parameterized protocols is especially challenging due to its "parameterized" feature, which brings…
String diagrams provide a convenient graphical framework which may be used for equational reasoning about morphisms of monoidal categories. However, unlike term rewriting, rewriting string diagrams results in shorter equational proofs,…
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…
A theory of recursive and corecursive definitions has been developed in higher-order logic (HOL) and mechanized using Isabelle. Least fixedpoints express inductive data types such as strict lists; greatest fixedpoints express coinductive…
Developments in semantic web technologies have promoted ontological encoding of knowledge from diverse domains. However, modelling many practical domains requires more expressive representations schemes than what the standard description…
In recent years, diagrammatic languages have been shown to be a powerful and expressive tool for reasoning about physical, logical, and semantic processes represented as morphisms in a monoidal category. In particular, categorical quantum…
Using a call-by-value functional language as an example, this article illustrates the use of coinductive definitions and proofs in big-step operational semantics, enabling it to describe diverging evaluations in addition to terminating…
The Circularity Principle was successfully applied for developing a coinductive proving technique, known as circular coinduction. In this paper, we show that the same principle can be used to develop an inductive proving technique. A main…
In this thesis, we present two approaches to a rigorous mathematical and algorithmic foundation of quantitative and statistical inference in constraint-based natural language processing. The first approach, called quantitative constraint…
Proof nets are a syntax for linear logic proofs which gives a coarser notion of proof equivalence with respect to syntactic equality together with an intuitive geometrical representation of proofs. In this paper we give an alternative…
Arguments are a fundamental aspect of human reasoning, in which claims are supported, challenged, and weighed against one another. We present an end-to-end large language model (LLM)-based system for reconstructing arguments from natural…
Conjecturing and theorem proving are activities at the center of mathematical practice and are difficult to separate. In this paper, we propose a framework for completing incomplete conjectures and incomplete proofs. The framework can turn…
Different types of reasoning impose different structural demands on representational systems, yet no systematic account of these demands exists across psychology, AI, and philosophy of mind. I propose a framework identifying four structural…
The likelihood for the parameters of a generalized linear mixed model involves an integral which may be of very high dimension. Because of this intractability, many approximations to the likelihood have been proposed, but all can fail when…
Traditional treatments of formal logic provide: 1. A syntax for formulas. 2. An inference relation between sets of formulas. 3. A rule for assigning meaning to formulas (semantics) that is sound with respect to the inference relation. First…
Large Language Models (LLMs) have shown strong performance in solving mathematical problems, with code-based solutions proving particularly effective. However, the best practice to leverage coding instruction data to enhance mathematical…
In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…
By adapting Salomaa's complete proof system for equality of regular expressions under the language semantics, Milner (1984) formulated a sound proof system for bisimilarity of regular expressions under the process interpretation he…
The ever-growing complexity of mathematical proofs makes their manual verification by mathematicians very cognitively demanding. Autoformalization seeks to address this by translating proofs written in natural language into a formal…
In type theory, coinductive types are used to represent processes, and are thus crucial for the formal verification of non-terminating reactive programs in proof assistants based on type theory, such as Coq and Agda. Currently, programming…