Related papers: A Labelled Sequent Calculus for BBI: Proof Theory …
Following G. Mints(Kluwer 2000 and draft 2013), we present terminating and bicomplete proof searches in multi-succedent sequent calculi for intuitionistic propositional logic, fragments of intuitionistic predicate logic and full…
We present a calculus providing a Curry-Howard correspondence to classical logic represented in the sequent calculus with explicit structural rules, namely weakening and contraction. These structural rules introduce explicit erasure and…
During the past decade, there has been an extensive investigation of the computational complexity of the consistent answers of Boolean conjunctive queries under primary key constraints. Much of this investigation has focused on…
We extend the synthetic theories of discrete and Gaussian categorical probability by introducing a diagrammatic calculus for reasoning about hybrid probabilistic models in which continuous random variables, conditioned on discrete ones,…
We propose a graph-based extension of Boolean logic called Boolean Graph Logic (BGL). Construing formula trees as the cotrees of cographs, we may state semantic notions such as evaluation and entailment in purely graph-theoretic terms,…
We introduce LAM, a subsystem of IMALL2 with restricted additive rules able to manage duplication linearly, called linear additive rules. LAM is presented as the type assignment system for a calculus endowed with copy constructors, which…
On the ground of a general theorem concerning the admissibility of the structural rules in sequent calculi with additional atomic rules, we develop a proof theoretic analysis for several extensions of the ${\bf G3[mic]}$ sequent calculi…
We present a novel method - LIBRE - to learn an interpretable classifier, which materializes as a set of Boolean rules. LIBRE uses an ensemble of bottom-up weak learners operating on a random subset of features, which allows for the…
The sequent calculus is a formalism for proving validity of statements formulated in First-Order Logic. It is routinely used in computer science modules on mathematical logic. Formal proofs in the sequent calculus are finite trees obtained…
We develop estimation for potentially high-dimensional additive structural equation models. A key component of our approach is to decouple order search among the variables from feature or edge selection in a directed acyclic graph encoding…
In this paper we explore the design of sequent calculi operating on graphs. For this purpose, we introduce a set of logical connectives allowing us to extend the correspondence between cographs and classical propositional formulas to any…
Scores based on Shapley values are widely used for providing explanations to classification results over machine learning models. A prime example of this is the influential SHAP-score, a version of the Shapley value that can help explain…
This paper presents complexity analysis and variational methods for inference in probabilistic description logics featuring Boolean operators, quantification, qualified number restrictions, nominals, inverse roles and role hierarchies.…
We provide a new sequent calculus that enjoys syntactic cut-elimination and strongly terminating backward proof search for the intuitionistic Strong L\"ob logic $\sf{iSL}$, an intuitionistic modal logic with a provability interpretation. A…
We present PBLean, a method for importing VeriPB pseudo-Boolean (PB) proof certificates into Lean 4. Key to our approach is reflection: a Boolean checker function whose soundness is fully proved in Lean and executed as compiled native code.…
In this paper we investigate the Curry-Howard correspondence for constructive modal logic in light of the gap between the proof equivalences enforced by the lambda calculi from the literature and by the recently defined winning strategies…
We introduce a combinatorial enumeration problem that is solved using generalized Catalan numbers. We also study generalizations of the Cycle Lemma beyond the computation of the generalized Catalan numbers.
Independence and conditional independence are fundamental concepts for reasoning about groups of random variables in probabilistic programs. Verification methods for independence are still nascent, and existing methods cannot handle…
We consider grammar-restricted exact learning of formulas and terms in finite variable logics. We propose a novel and versatile automata-theoretic technique for solving such problems. We first show results for learning formulas that…
We pose causal inference as the problem of learning to classify probability distributions. In particular, we assume access to a collection $\{(S_i,l_i)\}_{i=1}^n$, where each $S_i$ is a sample drawn from the probability distribution of $X_i…