Related papers: A Meta-Programming Approach to Realizing Dependent…
Differentiable logics are a family of quantitative logics originated in the machine learning literature. Because of their origin, differentiable logics often come equipped with analytic properties that guarantee that they are…
Understanding how Large Language Models (LLMs) perform logical reasoning internally remains a fundamental challenge. While prior mechanistic studies focus on identifying taskspecific circuits, they leave open the question of what…
Large Language Models (LLMs), excel in natural language understanding, but their capability for complex mathematical reasoning with an amalgamation of structured tables and unstructured text is uncertain. This study explores LLMs'…
In dependently typed programming, proofs of basic, structural properties can be embedded implicitly into programs and do not need to be written explicitly. Besides saving the effort of writing separate proofs, a most distinguishing and…
We extend the simply-typed guarded $\lambda$-calculus with discrete probabilities and endow it with a program logic for reasoning about relational properties of guarded probabilistic computations. This provides a framework for programming…
This paper presents a computational model for the cooperation of constraint domains and an implementation for a particular case of practical importance. The computational model supports declarative programming with lazy and possibly…
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…
Much of the current research and development in the field of automated reasoning builds on the infrastructure provided by the TPTP World. The TPTP language for logical formulae is central to the far-reaching adoption of the TPTP World. This…
We scale layered modal type theory to dependent types, introducing DeLaM, dependent layered modal type theory. This type theory is novel in that we have one uniform type theory in which we can not only compose and execute code, but also…
The demonstrated code-understanding capability of LLMs raises the question of whether they can be used for automated program verification, a task that demands high-level abstract reasoning about program properties that is challenging for…
We introduce a generalized logic programming paradigm where programs, consisting of facts and rules with the usual syntax, can be enriched by co-facts, which syntactically resemble facts but have a special meaning. As in coinductive logic…
A framework with sets of attacking arguments (SETAF) is an extension of the well-known Dung's Abstract Argumentation Frameworks (AAFs) that allows joint attacks on arguments. In this paper, we provide a translation from Normal Logic…
An approach for encoding abstract dialectical frameworks and their semantics into classical higher-order logic is presented. Important properties and semantic relationships are formally encoded and proven using the proof assistant…
The reasoning abilities are one of the most enigmatic and captivating aspects of large language models (LLMs). Numerous studies are dedicated to exploring and expanding the boundaries of this reasoning capability. However, tasks that embody…
The aim of staged compilation is to enable metaprogramming in a way such that we have guarantees about the well-formedness of code output, and we can also mix together object-level and meta-level code in a concise and convenient manner. In…
In this paper, we address program development by multiple different programmers (or programming teams), each working in different settings (programming languages or reasoning frameworks), but following a common specification; in particular,…
Large Language Models (LLMs) trained on petabytes of data are highly compressed repositories of a significant proportion of the knowledge accumulated and distilled so far. In this paper we study techniques to elicit this knowledge in the…
Practical checkers based on refinement types use the combination of implicit semantic sub-typing and parametric polymorphism to simplify the specification and automate the verification of sophisticated properties of programs. However, a…
The Teyjus system realizes the higher-order logic programming language$\lambda$Prolog by compiling programs into bytecode for an abstract machine and executing this translated form using a simulator for the machine. Teyjus supports a number…
Abductive logic programs offer a formalism to declaratively represent and reason about problems in a variety of areas: diagnosis, decision making, hypothetical reasoning, etc. On the other hand, logic program updates allow us to express…