Related papers: Reasoning with Higher-Order Abstract Syntax in a L…
This thesis develops a framework for formalizing reasoning about specifications of systems written in LF. This formalization centers around the development of a reasoning logic that can express the sorts of properties which arise in…
Both syntax-phonology and syntax-semantics interfaces in Higher Order Grammar (HOG) are expressed as axiomatic theories in higher-order logic (HOL), i.e. a language is defined entirely in terms of provability in the single logical system.…
Developing suitable formal semantics can be of great help in the understanding, design and implementation of a programming language, and act as a guide for software development tools like analyzers or partial evaluators. In this sense, full…
Dependently typed lambda calculi such as the Logical Framework (LF) can encode relationships between terms in types and can naturally capture correspondences between formulas and their proofs. Such calculi can also be given a logic…
Argumentation frameworks ($AF$s) have been a useful tool for approximate reasoning. The encoding method is an important approach to formally model $AF$s under related semantics. The aim of this paper is to develop the encoding method from…
There is a growing need for abstractions in logic specification languages such as FO(.) and ASP. One technique to achieve these abstractions are templates (sometimes called macros). While the semantics of templates are virtually always…
Motivated by applications in automated verification of higher-order functional programs, we develop a notion of constrained Horn clauses in higher-order logic and a decision problem concerning their satisfiability. We show that, although…
While Chain-of-Thought (CoT) prompting enhances the reasoning capabilities of large language models, the faithfulness of the generated rationales remains an open problem for model interpretability. We propose a novel theoretical lens for…
Many abstract interpretation frameworks and analyses for Prolog have been proposed, which seek to extract information useful for program optimization. Although motivated by practical considerations, notably making Prolog competitive with…
Large language models (LLMs) have achieved impressive proficiency on logic and programming tasks, often rivaling expert-level performance. However, generating functionally correct hardware description language (HDL) code from natural…
A framework and methodology---termed LogiKEy---for the design and engineering of ethical reasoners, normative theories and deontic logics is presented. The overall motivation is the development of suitable means for the control and…
We describe a Martin-L\"of-style dependent type theory, called Cocon, that allows us to mix the intensional function space that is used to represent higher-order abstract syntax (HOAS) trees with the extensional function space that…
In prior work, we showed that logic programming compilation can be given a proof-theoretic justification for generic abstract logic programming languages, and demonstrated this technique in the case of hereditary Harrop formulas and their…
Abstract interpretation, Hoare logic, and incorrectness (or reverse Hoare) logic are powerful techniques for static analysis of computer programs. All of them have been successfully extended to the quantum setting, but largely developed in…
This paper presents matching logic, a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives…
Logical frameworks provide natural and direct ways of specifying and reasoning within deductive systems. The logical framework LF and subsequent developments focus on finitary proof systems, making the formalization of circular proof…
Coinduction is a widely used technique for establishing behavioural equivalence of programs in higher-order languages. In recent years, the rise of languages with quantitative (e.g.~probabilistic) features has led to extensions of…
Argumentation is a very active research field of Artificial Intelligence concerned with the representation and evaluation of arguments used in dialogues between humans and/or artificial agents. Acceptability semantics of formal…
Chain-of-Thought (CoT) prompting has significantly improved the reasoning capabilities of large language models (LLMs). However, conventional CoT often relies on unstructured, flat reasoning chains that suffer from redundancy and suboptimal…
Formal verification provides strong guarantees of correctness of software, which are especially important in safety or security critical systems. Hoare logic is a widely used formalism for rigorous verification of software against…