相关论文: Many Logics, One Methodology: A Plea for Logical P…
Proof assistants play a dual role as programming languages and logical systems. As programming languages, proof assistants offer standard modularity mechanisms such as first-class functions, type polymorphism and modules. As logical…
A flexible infrastructure for normative reasoning is outlined. A small-scale demonstrator version of the envisioned system has been implemented in the proof assistant Isabelle/HOL by utilising the first authors universal logical reasoning…
Large language models (LLMs) have proven to be highly effective for solving complex reasoning tasks. Surprisingly, their capabilities can often be improved by iterating on previously generated solutions. In this context, a reasoning plan…
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…
Tremendous research effort has been dedicated over the years to thoroughly investigate non-monotonic reasoning. With the abundance of non-monotonic logical formalisms, a unified theory that enables comparing the different approaches is much…
We propose a new formalism for specifying and reasoning about problems that involve heterogeneous "pieces of information" -- large collections of data, decision procedures of any kind and complexity and connections between them. The essence…
We present a novel approach for teaching logic and the metatheory of logic to students who have some experience with functional programming. We define concepts in logic as a series of functional programs in the language of the proof…
The integration of lexical semantics and pragmatics in the analysis of the meaning of natural lan- guage has prompted changes to the global framework derived from Montague. In those works, the original lexicon, in which words were assigned…
Leveraging outputs from multiple large language models (LLMs) is emerging as a method for harnessing their power across a wide range of tasks while mitigating their capacity for making errors, e.g., hallucinations. However, current…
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…
Dialectical logic is the logic of dialectical processes. The goal of dialectical logic is to reveal the dynamical notions inherent in logical computational systems. The fundamental notions of proposition and truth-value in standard logic…
We present a generic framework that facilitates object level reasoning with logics that are encoded within the Higher Order Logic theorem proving environment of HOL Light. This involves proving statements in any logic using intuitive…
Logic programming languages present clear advantages in terms of declarativeness and conciseness. However, the ideas of logic programming have been met with resistance in other programming communities, and have not generally been adopted by…
This paper presents a new system of logic, LF, that is intended to be used as the foundation of the formalization of science. That is, deductive validity according to LF is to be used as the criterion for assessing what follows from the…
Deductive verification techniques based on program logics (i.e., the family of Floyd-Hoare logics) are a powerful approach for program reasoning. Recently, there has been a trend of increasing the expressive power of such logics by…
The probability theory is a well-studied branch of mathematics, in order to carry out formal reasoning about probability. Thus, it is important to have a logic, both for computation of probabilities and for reasoning about probabilities,…
Standpoint logics offer unified modal logic-based formalisms for representing multiple heterogeneous viewpoints. At the same time, many non-monotonic reasoning frameworks can be naturally captured using modal logics, in particular using the…
Large Language Models (LLMs) have demonstrated impressive capabilities in structured reasoning and symbolic tasks, with coding emerging as a particularly successful application. This progress has naturally motivated efforts to extend these…
Logical reasoning is central to human cognition and intelligence. It includes deductive, inductive, and abductive reasoning. Past research of logical reasoning within AI uses formal language as knowledge representation and symbolic…
The spread of misinformation, propaganda, and flawed argumentation has been amplified in the Internet era. Given the volume of data and the subtlety of identifying violations of argumentation norms, supporting information analytics tasks,…