arXiv subjects

Maria Osório

Publications and source records attributed to Maria Osório.

3 recordsLinked to original sources

arXiv2026

Bilateralism with incompatible proofs and refutations

Logical bilateralism challenges traditional concepts of logic by treating assertion and denial as independent yet opposed acts. While initially devised to justify classical logic, its constructive variants show that both acts admit intuitionistic interpretations. This paper presents a bilateral system where a formula cannot be both provable and refutable without contradiction, offering a framework for modelling epistemic entities, such as mathematical proofs and refutations, that exclude inconsistency. The logic is formalised through a bilateral natural deduction system with desirable proof-theoretic properties, including normalisation. We also introduce a base-extension semantics requiring explicit constructions of proofs and refutations while preventing them from being established for the same formula. The semantics is proven sound and complete with respect to the calculus. Finally, we show that our notion of refutation corresponds to David Nelson's constructive falsity, extending rather than revising intuitionistic logic and reinforcing the system's suitability for representing constructive epistemic reasoning.

cs.LO↗

arXiv2025

Bilateral base-extension semantics

Bilateralism is the position according to which assertion and rejection are conceptually independent speech acts. Logical bilateralism demands that systems of logic provide conditions for assertion and rejection that are not reducible to each other, which often leads to independent definitions of proof rules (for assertion) and dual proof rules, also called refutation rules (for rejection). Since it provides a critical account of what it means for something to be a proof or a refutation, bilateralism is often studied in the context of proof-theoretic semantics, an approach that aims to elucidate both the meaning of proofs (and refutations) and what kinds of semantics can be given if proofs (and refutations) are considered as basic semantic notions. The recent literature on bilateral proof-theoretic semantics has only dealt with the semantics of proofs and refutations, whereas we deal with semantics in terms of proofs and refutations. In this paper we present a bilateral version of base-extension semantics - one of the most widely studied proof-theoretic semantics - by allowing atomic bases to contain both atomic proof rules and atomic refutation rules. The semantics is shown to be sound and complete with respect to the bilateral dual intuitionistic logic 2Int. Structural similarities between atomic proofs and refutations also allow us to define duality notions for atomic rules, deductions and bases, which may then be used for the proof of bilateral semantic harmony results. Aside from enabling embeddings between different fragments of the language, bilateral semantic harmony is shown to be a restatement of the syntactic horizontal inversion principle, whose meaning-conferring character may now be interpreted as the requirement of preservation of harmony notions already present at the core of the semantics by inferences.

math.LO↗

arXiv2022

Can a Hebbian-like learning rule be avoiding the curse of dimensionality in sparse distributed data?

It is generally assumed that the brain uses something akin to sparse distributed representations. These representations, however, are high-dimensional and consequently they affect classification performance of traditional Machine Learning models due to "the curse of dimensionality". In tasks for which there is a vast amount of labeled data, Deep Networks seem to solve this issue with many layers and a non-Hebbian backpropagation algorithm. The brain, however, seems to be able to solve the problem with few layers. In this work, we hypothesize that this happens by using Hebbian learning. Actually, the Hebbian-like learning rule of Restricted Boltzmann Machines learns the input patterns asymmetrically. It exclusively learns the correlation between non-zero values and ignores the zeros, which represent the vast majority of the input dimensionality. By ignoring the zeros "the curse of dimensionality" problem can be avoided. To test our hypothesis, we generated several sparse datasets and compared the performance of a Restricted Boltzmann Machine classifier with some Backprop-trained networks. The experiments using these codes confirm our initial intuition as the Restricted Boltzmann Machine shows a good generalization performance, while the Neural Networks trained with the backpropagation algorithm overfit the training data.

cs.NE↗