arXiv subjects

João Marcos

Publications and source records attributed to João Marcos.

At least 19 recordsLinked to original sources

arXiv2026

Intrinsic and relative characterization results for logics with negative modalities

We introduce simulations for modal logics with subclassical negations and restoration modalities, establish an adequacy theorem, and prove intrinsic (Hennessy-Milner-type) and relative (Van Benthem-type) characterization results. These results identify each restorative language with the fragment of first-order logic invariant under its simulations and delineate the expressive profile of modal logics with non-classical negations.

math.LO↗

arXiv2026

Intuitionistic K is a Bisimulation-Invariant Fragment of Intuitionistic First-Order Logic

We define the notion of IK-bisimulation between the relational semantics for the intuitionistic modal logic IK, and prove that IK arises as the IK-bisimulation-invariant fragment of intuitionistic first-order logic. En route, we provide an intrinsic characterisation result of this logic by way of a Hennessy-Milner-style theorem and develop some intuitionistic first-order model theory, including intuitionistic analogues of Los's Theorem, elementary embeddings and countable saturation.

math.LO↗

arXiv2026

A method for the automated generation of proof exercises with comparable levels of proving complexity

The automated generation of exercises may substantially reduce the time educators devote to manual exercise design. A major obstacle to the integration of such automation into teaching practice, however, lies in the ability to control the difficulty of mechanically generated exercises. This paper presents a method for the automated generation of proof exercises with comparable levels of proving complexity. The method takes as input a proof exercise together with a set of rules that yield a proof of the exercise, and produces as output a set of proof exercises whose proving complexity is comparable to that of the input exercise. The approach focuses on mathematical proof exercises formulated in first-order languages, covering topics typically addressed in undergraduate Discrete Mathematics courses. We assess the proving complexity of these exercises by considering the effort required to solve them through informal proofs, and argue that this effort can be formally captured through cut-based tableau proofs that are free of logical symbols. The rules governing such proofs are obtained through a mechanizable extraction procedure introduced in this paper. By exploiting the analytic nature of these rules and the structure inherent in proofs constructed via tableau rules, we derive a computational procedure implementing the proposed method.

cs.LO↗

arXiv2026

DFIC: Towards a balanced facial image dataset for automatic ICAO compliance verification

Ensuring compliance with ISO/IEC and ICAO standards for facial images in machine-readable travel documents (MRTDs) is essential for reliable identity verification, but current manual inspection methods are inefficient in high-demand environments. This paper introduces the DFIC dataset, a novel comprehensive facial image dataset comprising around 58,000 annotated images and 2706 videos of more than 1000 subjects, that cover a broad range of non-compliant conditions, in addition to compliant portraits. Our dataset provides a more balanced demographic distribution than the existing public datasets, with one partition that is nearly uniformly distributed, facilitating the development of automated ICAO compliance verification methods. Using DFIC, we fine-tuned a novel method that heavily relies on spatial attention mechanisms for the automatic validation of ICAO compliance requirements, and we have compared it with the state-of-the-art aimed at ICAO compliance verification, demonstrating improved results. DFIC dataset is now made public (https://github.com/visteam-isr-uc/DFIC) for the training and validation of new models, offering an unprecedented diversity of faces, that will improve both robustness and adaptability to the intrinsically diverse combinations of faces and props that can be presented to the validation system. These results emphasize the potential of DFIC to enhance automated ICAO compliance methods but it can also be used in many other applications that aim to improve the security, privacy, and fairness of facial recognition systems.

cs.CV↗

arXiv2024

Adding an Implication to Logics of Perfect Paradefinite Algebras

Perfect paradefinite algebras are De Morgan algebras expanded with an operation that allows for the full behavior of classical negation to be restored. They form a variety that is term-equivalent to the variety of involutive Stone algebras. Their associated multiple-conclusion (Set-Set) and single-conclusion (Set-Fmla) order-preserving logics are non-algebraizable self-extensional logics of formal inconsistency and undeterminedness determined by a six-valued matrix, studied in depth by Gomes et al. (2022) from both the algebraic and the proof-theoretical perspectives. In the present paper, we continue that study by investigating directions for conservatively expanding these logics with an implication connective (essentially, one that admits the deduction-detachment theorem). We first consider logics given by very simple and manageable non-deterministic semantics whose implication (in isolation) is classical. These, nevertheless, fail to be self-extensional. We then consider the implication realized by the relative pseudo-complement over the six-valued perfect paradefinite algebra. Our strategy is to expand the language of the latter algebra with this connective and study the (self-extensional) Set-Set and Set-Fmla order-preserving and top-assertional logics of the variety induced by the resulting algebra. We provide axiomatizations for such new variety and for such logics, drawing parallels with the class of symmetric Heyting algebras and with Moisil's 'symmetric modal logic'. For the Set-Set logic, in particular, the axiomatization we obtain is analytic. We close by studying interpolation properties for these logics and concluding that the new variety has the Maehara amalgamation property.

cs.LO↗

arXiv2023

Proceedings 11th International Workshop on Theorem Proving Components for Educational Software

The ThEdu series pursues the smooth transition from an intuitive way of doing mathematics at secondary school to a more formal approach to the subject in STEM education, while favouring software support for this transition by exploiting the power of theorem-proving technologies. What follows is a brief description of how the present volume contributes to this enterprise. The 11th International Workshop on Theorem Proving Components for Educational Software (ThEdu'22), was a satellite event of the 8th Federated Logic Conference (FLoC 2022), July 31-August 12, 2022, Haifa, Israel ThEdu'22 was a vibrant workshop, with two invited talk by Thierry Dana-Picard (Jerusalem College of Technology, Jerusalem, Israel) and Yoni Zohar (Bar Ilan University, Tel Aviv, Israel) and four contributions. An open call for papers was then issued, and attracted seven submissions. Those submissions have been accepted by our reviewers, who jointly produced at least three careful reports on each of the contributions. The resulting revised papers are collected in the present volume. The contributions in this volume are a faithful representation of the wide spectrum of ThEdu, ranging from those more focused on the automated deduction research, not losing track of the possible applications in an educational setting, to those focused on the applications, in educational settings, of automated deduction tools and methods. We, the volume editors, hope that this collection of papers will further promote the development of theorem-proving based software, and that it will allow to improve the mutual understanding between computer scientists, mathematicians and stakeholders in education. While this volume goes to press, the next edition of the ThEdu workshop is being prepared: ThEdu'23 will be a satellite event of the 29th international Conference on Automated Deduction (CADE 2023), July 1-4, 2023, Rome, Italy.

cs.LO↗

arXiv2022

Finite two-dimensional proof systems for non-finitely axiomatizable logics

The characterizing properties of a proof-theoretical presentation of a given logic may hang on the choice of proof formalism, on the shape of the logical rules and of the sequents manipulated by a given proof system, on the underlying notion of consequence, and even on the expressiveness of its linguistic resources and on the logical framework into which it is embedded. Standard (one-dimensional) logics determined by (non-deterministic) logical matrices are known to be axiomatizable by analytic and possibly finite proof systems as soon as they turn out to satisfy a certain constraint of sufficient expressiveness. In this paper we introduce a recipe for cooking up a two-dimensional logical matrix (or B-matrix) by the combination of two (possibly partial) non-deterministic logical matrices. We will show that such a combination may result in B-matrices satisfying the property of sufficient expressiveness, even when the input matrices are not sufficiently expressive in isolation, and we will use this result to show that one-dimensional logics that are not finitely axiomatizable may inhabit finitely axiomatizable two-dimensional logics, becoming, thus, finitely axiomatizable by the addition of an extra dimension. We will illustrate the said construction using a well-known logic of formal inconsistency called mCi. We will first prove that this logic is not finitely axiomatizable by a one-dimensional (generalized) Hilbert-style system. Then, taking advantage of a known 5-valued non-deterministic logical matrix for this logic, we will combine it with another one, conveniently chosen so as to give rise to a B-matrix that is axiomatized by a two-dimensional Hilbert-style system that is both finite and analytic.

cs.LO↗

arXiv2022

On Logics of Perfect Paradefinite Algebras

The present study shows how to enrich De Morgan algebras with a perfection operator that allows one to express the Boolean properties of negation-consistency and negation-determinedness. The variety of perfect paradefinite algebras thus obtained (PP-algebras) is shown to be term-equivalent to the variety of involutive Stone algebras, introduced by R. Cignoli and M. Sagastume, and more recently studied from a logical perspective by M. Figallo-L. Cantú and by S. Marcelino-U. Rivieccio. This equivalence plays an important role in the investigation of the 1-assertional logic and of the order-preserving logic associated to PP-algebras. The latter logic (here called PP<=) is characterized by a single 6-valued matrix and is shown to be a Logic of Formal Inconsistency and Formal Undeterminedness. We axiomatize PP<= by means of an analytic finite Hilbert-style calculus, and we present an axiomatization procedure that covers the logics corresponding to other classes of De Morgan algebras enriched by a perfection operator.

math.LO↗

arXiv2022

Proceedings 10th International Workshop on Theorem Proving Components for Educational Software

This EPTCS volume contains the proceedings of the ThEdu'21 workshop, promoted on 11 July 2021, as a satellite event of CADE-28. Due to the COVID-19 pandemic, CADE-28 and all its co-located events happened as virtual events. ThEdu'21 was a vibrant workshop, with an invited talk by Gilles Dowek (ENS Paris-Saclay), eleven contributions, and one demonstration. After the workshop an open call for papers was issued and attracted 10 submissions, 7 of which have been accepted by the reviewers, and collected in the present post-proceedings volume. The ThEdu series pursues the smooth transition from an intuitive way of doing mathematics at secondary school to a more formal approach to the subject in STEM education, while favouring software support for this transition by exploiting the power of theorem-proving technologies. The volume editors hope that this collection of papers will further promote the development of theorem-proving based software, and that it will collaborate on improving mutual understanding between computer scientists, mathematicians and stakeholders in education.

cs.LO↗

arXiv2021

Proof Search on Bilateralist Judgments over Non-deterministic Semantics

The bilateralist approach to logical consequence maintains that judgments of different qualities should be taken into account in determining what-follows-from-what. We argue that such an approach may be actualized by a two-dimensional notion of entailment induced by semantic structures that also accommodate non-deterministic and partial interpretations, and propose a proof-theoretical apparatus to reason over bilateralist judgments using symmetrical two-dimensional analytical Hilbert-style calculi. We also provide a proof-search algorithm for finite analytic calculi that runs in at most exponential time, in general, and in polynomial time when only rules having at most one formula in the succedent are present in the concerned calculus.

cs.LO↗

arXiv2020

Proceedings 9th International Workshop on Theorem Proving Components for Educational Software

The 9th International Workshop on Theorem-Proving Components for Educational Software (ThEdu'20) was scheduled to happen on June 29 as a satellite of the IJCAR-FSCD 2020 joint meeting, in Paris. The COVID-19 pandemic came by surprise, though, and the main conference was virtualised. Fearing that an online meeting would not allow our community to fully reproduce the usual face-to-face networking opportunities of the ThEdu initiative, the Steering Committee of ThEdu decided to cancel our workshop. Given that many of us had already planned and worked for that moment, we decided that ThEdu'20 could still live in the form of an EPTCS volume. The EPTCS concurred with us, recognising this very singular situation, and accepted our proposal of organising a special issue with papers submitted to ThEdu'20. An open call for papers was then issued, and attracted five submissions, all of which have been accepted by our reviewers, who produced three careful reports on each of the contributions. The resulting revised papers are collected in the present volume. We, the volume editors, hope that this collection of papers will help further promoting the development of theorem-proving-based software, and that it will collaborate to improve the mutual understanding between computer mathematicians and stakeholders in education. With some luck, we would actually expect that the very special circumstances set up by the worst sanitary crisis in a century will happen to reinforce the need for the application of certified components and of verification methods for the production of educational software that would be available even when the traditional on-site learning experiences turn out not to be recommendable.

cs.AI↗

arXiv2020

Proceedings 8th International Workshop on Theorem Proving Components for Educational Software

This EPTCS volume contains the proceedings of the ThEdu'19 workshop, promoted on August 25, 2019, as a satellite event of CADE-27, in Natal, Brazil. Representing the eighth installment of the ThEdu series, ThEdu'19 was a vibrant workshop, with an invited talk by Sarah Winkler, four contributions, and the first edition of a Geometry Automated Provers Competition. After the workshop an open call for papers was issued and attracted seven submissions, six of which have been accepted by the reviewers, and collected in the present post-proceedings volume. The ThEdu series pursues the smooth transition from an intuitive way of doing mathematics at secondary school to a more formal approach to the subject in STEM education, while favoring software support for this transition by exploiting the power of theorem-proving technologies. The volume editors hope that this collection of papers will further promote the development of theorem-proving-based software, and that it will collaborate on improving mutual understanding between computer mathematicians and stakeholders in education.

cs.LO↗

arXiv2019

What is a logical theory? On theories containing assertions and denials

The standard notion of formal theory, in Logic, is in general biased exclusively towards assertion: it commonly refers only to collections of assertions that any agent who accepts the generating axioms of the theory should also be committed to accept. In reviewing the main abstract approaches to the study of logical consequence, we point out why this notion of theory is unsatisfactory at multiple levels, and introduce a novel notion of theory that attacks the shortcomings of the received notion by allowing one to take both assertions and denials on a par. This novel notion of theory is based on a bilateralist approach to consequence operators, which we hereby introduce, and whose main properties we investigate in the present paper.

math.LO↗

arXiv2018

Combining fragments of classical logic: When are interaction principles needed?

We investigate the combination of fragments of classical logic as a way of conservatively extending a given Boolean logic by the addition of new connectives, and we precisely characterize the circumstances in which such a combination produces the corresponding fragment of classical logic over the signature containing connectives from both fragments given as input. If the thereby produced combined fragment is only incompletely characterized by the components given as input, this means that connectives from one component need to interact with connectives from the other component, giving rise to interaction principles. The main contributions strongly rely on the (well-known) description of the 2-valued clones made by Post, on the (not so well-known) axiomatization procedures for 2-valued matrices laid out by Rautenberg, and on Avron's non-deterministic matrices, which have (recently) been used to produce a significant advance on the understanding of the semantics of fibring.

cs.LO↗

arXiv2018

Algebraic Semantics for Nelson's Logic S

Besides the better-known Nelson's Logic and Paraconsistent Nelson's Logic, in "Negation and separation of concepts in constructive systems" (1959), David Nelson introduced a logic called S with the aim of analyzing the constructive content of provable negation statements in mathematics. Motivated by results from Kleene, in "On the Interpretation of Intuitionistic Number Theory" (1945), Nelson investigated a more symmetric recursive definition of truth, according to which a formula could be either primitively verified or refuted. The logic S was defined by means of a calculus lacking the contraction rule and having infinitely many schematic rules, and no semantics was provided. This system received little attention from researchers and it even remained unnoticed that on its original presentation it was inconsistent. Fortunately, the inconsistency was caused by typos and by a rule whose hypothesis and conclusion were swapped.We investigate in the present study a corrected version of the logic S, and focus at its propositional fragment, showing that it is algebraizable (in fact, implicative) with respect to a certain special class of involutive residuated lattices. We thus introduce the first (algebraic) semantics for S as well as a finite Hilbert-style calculus equivalent to Nelson's presentation. We also compare S with the other two above-mentioned logics of the Nelson family.

math.LO↗

arXiv2018

Semi-BCI Algebras

The notion of semi-BCI algebras is introduced and some of its properties are investigated. This algebra is another generalization for BCI-algebras. It arises from the "intervalization" of BCI algebras. Semi-BCI have a similar structure to Pseudo-BCI algebras however they are not the same. In this paper we also provide an investigation on the similarity between these classes of algebras by showing how they relate to the process of intervalization.

cs.LO↗

arXiv2017

Sequent systems for negative modalities

Non-classical negations may fail to be contradictory-forming operators in more than one way, and they often fail also to respect fundamental meta-logical properties such as the replacement property. Such drawbacks are witnessed by intricate semantics and proof systems, whose philosophical interpretations and computational properties are found wanting. In this paper we investigate congruential non-classical negations that live inside very natural systems of normal modal logics over complete distributive lattices; these logics are further enriched by adjustment connectives that may be used for handling reasoning under uncertainty caused by inconsistency or undeterminedness. Using such straightforward semantics, we study the classes of frames characterized by seriality, reflexivity, functionality, symmetry, transitivity, and some combinations thereof, and discuss what they reveal about sub-classical properties of negation. To the logics thereby characterized we apply a general mechanism that allows one to endow them with analytic ordinary sequent systems, most of which are even cut-free. We also investigate the exact circumstances that allow for classical negation to be explicitly defined inside our logics.

cs.LO↗

arXiv2017

Merging fragments of classical logic

We investigate the possibility of extending the non-functionally complete logic of a collection of Boolean connectives by the addition of further Boolean connectives that make the resulting set of connectives functionally complete. More precisely, we will be interested in checking whether an axiomatization for Classical Propositional Logic may be produced by merging Hilbert-style calculi for two disjoint incomplete fragments of it. We will prove that the answer to that problem is a negative one, unless one of the components includes only top-like connectives.

cs.LO↗