Related papers: An Abstract Algebraic Logic View on Judgment Aggre…
Supervised learning has gone beyond the expected risk minimization framework. Central to most of these developments is the introduction of more general aggregation functions for losses incurred by the learner. In this paper, we turn towards…
Abstract reasoning, i.e., inferring complicated patterns from given observations, is a central building block of artificial general intelligence. While humans find the answer by either eliminating wrong candidates or first constructing the…
The present work presents some results about the categorial relation between logics and its categories of structures. A (propositional, finitary) logic is a pair given by a signature and Tarskian consequence relation on its formula algebra.…
Mathematical reasoning is a primary indicator of large language models (LLMs) intelligence. However, existing LLMs exhibit failures of robustness and generalization. This paper attributes these deficiencies to spurious reasoning, i.e.,…
Formal argumentation is being used increasingly in artificial intelligence as an effective and understandable way to model potentially conflicting pieces of information, called arguments, and identify so-called acceptable arguments…
Existing multi-expert LLM systems gather diverse perspectives but combine them through simple aggregation, obscuring which arguments drove the final decision. We introduce ARGORA, a framework that organizes multi-expert discussions into…
This paper studies algebras arising as algebraic semantics for logics used to model reasoning with incomplete or inconsistent information. In particular we study, in a uniform way, varieties of bilattices equipped with additional…
Most non-classical logics are subclassical, that is, every inference/theorem they validate is also valid classically. A notable exception is the three-valued propositional Logic of Ordinary Discourse (OL) proposed and extensively motivated…
Algebraic theories, sometimes called equational theories, are syntactic notions given by finitary operations and equations, such as monoids, groups, and rings. There is a well-known category-theoretic treatment of them that algebraic…
We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using…
Using the theory of coalgebra, we introduce a uniform framework for adding modalities to the language of propositional geometric logic. Models for this logic are based on coalgebras for an endofunctor on some full subcategory of the…
In this paper, we propose a variant of Answer Set Programming (ASP) with evaluable functions that extends their application to sets of objects, something that allows a fully logical treatment of aggregates. Formally, we start from the…
We introduce a novel method to aggregate Bipolar Argumentation (BA) Frameworks expressing opinions by different parties in debates. We use Bipolar Assumption-based Argumentation (ABA) as an all-encompassing formalism for BA under different…
In a seminal work, K. Segerberg introduced a deontic logic called DAL to investigate normative reasoning over actions. DAL marked the beginning of a new area of research in Deontic Logic by shifting the focus from deontic operators on…
Motivated by questions like: which spatial structures may be characterized by means of modal logic, what is the logic of space, how to encode in modal logic different geometric relations, topological logic provides a framework for studying…
These are lecture notes on the algebraic approach to regular languages. The classical algebraic approach is for finite words; it uses semigroups instead of automata. However, the algebraic approach can be extended to structures beyond…
Abstract algebraic logic is a theory that provides general tools for the algebraic study of arbitrary propositional logics. According to this theory, every logic L is associated with a matrix semantics Mod*(L). This paper is a contribution…
Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such…
We present principles of algebraic diversity (AD), a group-theoretic approach to signal processing exploiting signal symmetry to extract more information per observation, complementing classical methods that use temporal and spatial…
In this paper we investigate two logics from an algebraic point of view. The two logics are: MALL (multiplicative-additive Linear Logic) and LL (classical Linear Logic). Both logics turn out to be strongly algebraizable in the sense of Blok…