Related papers: Case Studies in Formal Reasoning About Lambda-Calc…
This note clarifies the concept of syntax and semantics and their relationships. Today, a lot of confusion arises from the fact that the word "semantics" is used in different meanings. We discuss a general approach at defining semantics…
The algebraic lambda calculus and the linear algebraic lambda calculus are two extensions of the classical lambda calculus with linear combinations of terms. They arise independently in distinct contexts: the former is a fragment of the…
Large Language Models (LLMs) are often described as instances of foundation models that possess strong generalization obeying scaling laws, and therefore transfer robustly across various conditions in few- or zero-shot manner. Such claims…
In this paper I will develop a lambda-term calculus, lambda-2Int, for a bi-intuitionistic logic and discuss its implications for the notions of sense and denotation of derivations in a bilateralist setting. Thus, I will use the Curry-Howard…
In this thesis, a comprehensive formalization of Milner's Calculus of Communicating Systems (also known as CCS) has been done in HOL theorem prover (HOL4), based on an old work in HOL88. This includes all classical properties of strong/weak…
The formalisation of mathematics is continuing rapidly, however combinatorics continues to present challenges to formalisation efforts, such as its reliance on techniques from a wide range of other fields in mathematics. This paper presents…
We report on yet another formalization of the Church-Rosser property in lambda-calculi, carried out with the proof environment Beluga. After the well-known proofs of confluence for beta-reduction in the untyped settings, with and without…
We present a new modular proof method of termination for second-order computation, and report its implementation SOL. The proof method is useful for proving termination of higher-order foundational calculi. To establish the method, we use a…
Autoformalization, the automatic translation of mathematical content from natural language into machine-verifiable formal languages, has seen significant progress driven by advances in large language models (LLMs). Nonetheless, a primary…
We study the generalization abilities of language models when translating natural language into formal specifications with complex semantics. In particular, we fine-tune language models on three datasets consisting of English sentences and…
Finite Automata (FAs) are fundamental components in the domains of programming languages. For instance, regular expressions, which are pivotal in languages such as JavaScript and Python, are frequently implemented using FAs. Finite…
This reports introduces a novel sound and complete semantics for first order intuitionistic logic, in the framework of category theory and by the computational interpretation of the logic based on the so-called Curry-Howard isomorphism.…
This invited paper presents an overview of an ongoing research program aimed at extending the Curry-Howard-Lambek correspondence to quantum computation. We explore two key frameworks that provide both logical and computational foundations…
In this article we show that hybrid type-logical grammars are a fragment of first-order linear logic. This embedding result has several important consequences: it not only provides a simple new proof theory for the calculus, thereby…
The primary goal of this paper is to present a unified way to transform the syntax of a logic system into certain initial algebraic structure so that it can be studied algebraically. The algebraic structures which one may choose for this…
Mission-time Linear Temporal Logic (MLTL) is rapidly increasing in popularity as a specification logic, e.g., for runtime verification and model checking, driving a need for a trustworthy tool base for analyzing MLTL. In this work, we…
Argumentation frameworks ($AF$s) have been extensively developed, but existing higher-order bipolar $AF$s suffer from critical limitations: attackers and supporters are restricted to arguments, multi-valued and fuzzy semantics lack unified…
We introduce syntactic modal operator $\BOX$ for \textit{being a thesis} into first-order logic. This logic is a modern realization of R. Carnap's old ideas on modality, as logical necessity (J. Symb. Logic, 1946) \cite{Ca46}. We place it…
One can perform equational reasoning about computational effects with a purely functional programming language thanks to monads. Even though equational reasoning for effectful programs is desirable, it is not yet mainstream. This is partly…
The lambda-PRK-calculus is a typed lambda-calculus that exploits the duality between the notions of proof and refutation to provide a computational interpretation for classical propositional logic. In this work, we extend lambda-PRK to…