Related papers: Hybrid: A Definitional Two-Level Approach to Reaso…
An inductive inference system for proving validity of formulas in the initial algebra $T_{\mathcal{E}}$ of an order-sorted equational theory $\mathcal{E}$ is presented. It has 20 inference rules, but only 9 of them require user interaction;…
We propose a hybrid architecture for systematically computing robust visual explanation(s) encompassing hypothesis formation, belief revision, and default reasoning with video data. The architecture consists of two tightly integrated…
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…
Relational program verification is a variant of program verification where one can reason about two programs and as a special case about two executions of a single program on different inputs. Relational program verification can be used for…
Classical higher-order logic, when utilized as a meta-logic in which various other (classical and non-classical) logics can be shallowly embedded, is well suited for realising a universal logic reasoning approach. Universal logic reasoning…
In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…
We use Dedukti as a logical framework for interoperability. We use automated tools to translate different developments made in HOL and in Coq to Dedukti, and we combine them to prove new results. We illustrate our approach with a concrete…
Standpoint logic is a recently proposed formalism in the context of knowledge integration, which advocates a multi-perspective approach permitting reasoning with a selection of diverse and possibly conflicting standpoints rather than…
Proof assistants offer tactics to apply proof by induction, but these tactics rely on inputs given by human engineers. To automate this laborious process, we developed SeLFiE, a boolean query language to represent experienced users'…
Dependent type theory gives an expressive type system facilitating succinct formalizations of mathematical concepts. In practice, it is mainly used for interactive theorem proving with intensional type theories, with PVS being a notable…
Chain-of-Thought (CoT) prompting has been widely recognized for its ability to enhance reasoning capabilities in large language models (LLMs). However, our study reveals a surprising contradiction to this prevailing perspective within the…
Despite recent advances in automating theorem proving in full first-order theories, inductive reasoning still poses a serious challenge to state-of-the-art theorem provers. The reason for that is that in first-order logic induction requires…
Recently an extension to higher-order logic -- called DHOL -- was introduced, enriching the language with dependent types, and creating a powerful extensional type theory. In this paper we propose two ways how choice can be added to DHOL.…
Description logics (DLs) are standard knowledge representation languages for modelling ontologies, i.e. knowledge about concepts and the relations between them. Unfortunately, DL ontologies are difficult to learn from data and…
We present a mechanized embedding of higher-order logic (HOL) and algebraic data types (ADT) into first-order logic with ZFC axioms. We implement this in the Lisa proof assistant for schematic first-order logic and its library based on…
We propose cognitive prompting as a novel approach to guide problem-solving in large language models (LLMs) through structured, human-like cognitive operations, such as goal clarification, decomposition, filtering, abstraction, and pattern…
Higher-level cognition includes logical reasoning and the ability of question answering with common sense. The RatioLog project addresses the problem of rational reasoning in deep question answering by methods from automated deduction and…
Recent advancements in multimodal large language models (MLLMs) have demonstrated exceptional performance in multimodal perception and understanding. However, leading open-source MLLMs exhibit significant limitations in complex and…
In a previous paper, a tableau calculus has been presented, which constitute a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work extends such a calculus to multi-modal…
Building rules on top of ontologies is the ultimate goal of the logical layer of the Semantic Web. To this aim an ad-hoc mark-up language for this layer is currently under discussion. It is intended to follow the tradition of hybrid…