Related papers: An Abstract Algebraic Logic View on Judgment Aggre…
Complexity and decidability of logics is a major research area involving a huge range of different logical systems. This calls for a unified and systematic approach for the field. We introduce a research program based on an algebraic…
Recent studies have shown that large language models (LLMs), especially smaller ones, often lack robustness in grade school math (GSM) reasoning. In particular, they tend to experience performance drops when faced with distribution shifts,…
We introduce and develop propositional continuous intuitionistic logic and propositional continuous affine logic via complete algebraic semantics. Our approach centres on AC-algebras, which are algebras $USC(\mathcal{L})$ of sup-preserving…
We evaluate two large language models (LLMs) ability to perform argumentative reasoning. We experiment with argument mining (AM) and argument pair extraction (APE), and evaluate the LLMs' ability to recognize arguments under progressively…
In a previous publication, we introduced an abstract logic via an abstract notion of quantifier. Drawing upon concepts from categorical logic, this abstract logic interprets formulas from context as subobjects in a specific category, e.g.,…
We study an extension of \g propositional logic whose corresponding algebra is an ordered Abelian group. Then we expand the ideas to first-order case of this logic.
Since the discovery of critical mistakes in Rauszer's work on bi-intuitionistic logics, solid foundations for these have progressively been rebuilt. However, the algebraic treatment of these logics has not yet been tended to. We fill this…
The Abstraction and Reasoning Corpus (ARC) aims at benchmarking the performance of general artificial intelligence algorithms. The ARC's focus on broad generalization and few-shot learning has made it difficult to solve using pure machine…
With help of a compact Prolog-based theorem prover for Intuitionistic Propositional Logic, we synthesize minimal assumptions under which a given formula formula becomes a theorem. After applying our synthesis algorithm to cover basic…
The framework of quantitative equational logic has been successfully applied to reason about algebras whose carriers are metric spaces and operations are nonexpansive. We extend this framework in two orthogonal directions: algebras endowed…
Abstract Dialectical Frameworks (ADFs) generalize Dung's argumentation frameworks allowing various relationships among arguments to be expressed in a systematic way. We further generalize ADFs so as to accommodate arbitrary acceptance…
Weighted monadic second-order logic is a weighted extension of monadic second-order logic that captures exactly the behaviour of weighted automata. Its semantics is parameterized with respect to a semiring on which the values that weighted…
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…
This chapter presents a state-of-the-art survey of relationships, traditionally referred to as `bridges', between interpolation properties for propositional logics -- including superintuitionistic, modal, and substructural logics -- and…
Large Language Models (LLMs) often struggle with deductive judgment in syllogistic reasoning, systematically conflating semantic plausibility with formal validity a phenomenon known as content effect. This bias persists even when models…
We introduce algebraic machine reasoning, a new reasoning framework that is well-suited for abstract reasoning. Effectively, algebraic machine reasoning reduces the difficult process of novel problem-solving to routine algebraic…
Typing of lambda-terms in Elementary and Light Affine Logic (EAL, LAL, resp.) has been studied for two different reasons: on the one hand the evaluation of typed terms using LAL (EAL, resp.) proof-nets admits a guaranteed polynomial…
Autoformalization plays a crucial role in formal mathematical reasoning by enabling the automatic translation of natural language statements into formal languages. While recent advances using large language models (LLMs) have shown…
G\"odel modal logics can be seen as extenions of intutionistic modal logics with the prelinearity axiom. In this paper we focus on the algebraic and relational semantics for G\"odel modal logics that leverages on the duality between finite…
Large language models (LLMs) demonstrate strong performance in math reasoning benchmarks, but their performance varies inconsistently across problems with varying levels of difficulty. This paper describes Adaptive Multi-Expert Reasoning…