Related papers: A Labelled Sequent Calculus for BBI: Proof Theory …
Classification is an important task in many fields including biomedical research and machine learning. Traditionally, a classification rule is constructed based a bunch of labeled data. Recently, due to technological innovation and…
Display calculi are generalized sequent calculi which enjoy a `canonical' cut elimination strategy. That is, their cut elimination is uniformly obtained by verifying the assumptions of a meta-theorem, and is preserved by adding or removing…
Answering Boolean conjunctive queries over the guarded fragment is decidable, however, as yet no practical decision procedure exists. Meanwhile, ordered resolution, as a practically oriented algorithm, is widely used in state-of-art modern…
We introduce and investigate symbolic proof systems for Quantified Boolean Formulas (QBF) operating on Ordered Binary Decision Diagrams (OBDDs). These systems capture QBF solvers that perform symbolic quantifier elimination, and as such…
Linear rules have played an increasing role in structural proof theory in recent years. It has been observed that the set of all sound linear inference rules in Boolean logic is already coNP-complete, i.e. that every Boolean tautology can…
Constraint-based learning reduces the burden of collecting labels by having users specify general properties of structured outputs, such as constraints imposed by physical laws. We propose a novel framework for simultaneously learning these…
In this paper we present a theorem proving methodology for a restricted but significant fragment of the conditional language made up of (boolean combinations of) conditional statements with unnested antecedents. The method is based on the…
Cayley's formula is a fundamental result in combinatorics that counts the number of labeled trees on n vertices. While existing proofs use approaches such as Prufer sequences and the Matrix-Tree Theorem, we give a combinatorial proof that…
Labelled tableaux have been a traditional approach to define satisfiability checking procedures for Modal Logics. In many cases, they can also be used to obtain tight complexity bounds and lead to efficient implementations of reasoning…
The term ``Boolean category'' should be used for describing an object that is to categories what a Boolean algebra is to posets. More specifically, a Boolean category should provide the abstract algebraic structure underlying the proofs in…
We describe a new, generally applicable strategy for the systematic construction of basis invariants (BIs). Our method allows one to count the number of mutually independent BIs and gives controlled access to the interrelations (syzygies)…
In this paper, we define a multi-type calculus for inquisitive logic, which is sound, complete and enjoys Belnap-style cut-elimination and subformula property. Inquisitive logic is the logic of inquisitive semantics, a semantic framework…
Exploiting label correlations is important to multi-label classification. Previous methods capture the high-order label correlations mainly by transforming the label matrix to a latent label space with low-rank matrix factorization.…
The application of binary matrices are numerous. Representing a matrix as a mixture of a small collection of latent vectors via low-rank decomposition is often seen as an advantageous method to interpret and analyze data. In this work, we…
Recent work proposed the computation of so-called PI-explanations of Naive Bayes Classifiers (NBCs). PI-explanations are subset-minimal sets of feature-value pairs that are sufficient for the prediction, and have been computed with…
A binarization of a bounded variable $x$ is a linear formulation with variables $x$ and additional binary variables $y_1,\dots, y_k$, so that integrality of $x$ is implied by the integrality of $y_1,\dots, y_k$. A binary extended…
Consequence-based reasoning can be used to construct proofs that explain entailments of description logic (DL) ontologies. In the literature, one can find multiple consequence-based calculi for reasoning in the $\mathcal{EL}$ family of DLs,…
We introduce a sequent calculus with a simple restriction of Lambek's product rules that precisely captures the classical Tamari order, i.e., the partial order on fully-bracketed words (equivalently, binary trees) induced by a…
We present a new perspective on the popular multi-class algorithmic techniques of one-vs-all and error correcting output codes. Rather than studying the behavior of these techniques for supervised learning, we establish a connection between…
We establish a formal correspondence between resource calculi an appropriate linear multicategories. We consider the cases of (symmetric) representable, symmetric closed and autonomous multicategories. For all these structures, we prove…