Related papers: CERES for First-Order Schemata
The preferential conditional logic PCL, introduced by Burgess, and its extensions are studied. First, a natural semantics based on neighbourhood models, which generalise Lewis' sphere models for counterfactual logics, is proposed. Soundness…
We describe a method for inverting Gentzen's cut-elimination in classical first-order logic. Our algorithm is based on first computign a compressed representation of the terms present in the cut-free proof and then cut-formulas that realize…
Counterfactual explanations (CEs) provide an intuitive way to understand recommender systems by identifying minimal modifications to user-item interactions that alter recommendation outcomes. Existing CE methods for recommender systems,…
We study cut elimination for a multifocused variant of full linear logic in the sequent calculus. The multifocused normal form of proofs yields problems that do not appear in a standard focused system, related to the constraints in grouping…
The coresets approach, also called subsampling or subset selection, aims to select a subsample as a surrogate for the observed sample and has found extensive applications in large-scale data analysis. Existing coresets methods construct the…
First-order logic has been established as an important tool for modeling and verifying intricate systems such as distributed protocols and concurrent systems. These systems are parametric in the number of nodes in the network or the number…
Herbrand's theorem is one of the most fundamental insights in logic. From the syntactic point of view it suggests a compact representation of proofs in classical first- and higher-order logic by recording the information which instances…
The key to the proof-theoretic study of a logic is a proof calculus with a subformula property. Many different proof formalisms have been introduced (e.g. sequent, nested sequent, labelled sequent formalisms) in order to provide such…
This thesis introduces the "method of structural refinement", which serves as a means of transforming the relational semantics of a modal and/or constructive logic into an 'economical' proof system by connecting two proof-theoretic…
Cut-elimination is the bedrock of proof theory with a multitude of applications from computational interpretations to proof analysis. It is also the starting point for important meta-theoretical investigations including decidability,…
Basic proof-search tactics in logic and type theory can be seen as the root-first applications of rules in an appropriate sequent calculus, preferably without the redundancies generated by permutation of rules. This paper addresses the…
Prior work suggests that neural networks tend to learn low-order moments of the data distribution first, before moving on to higher-order correlations. In this work, we derive a novel closed-form concept erasure method, QLEACE, which…
The calculus of looping sequences is a formalism for describing the evolution of biological systems by means of term rewriting rules. We enrich this calculus with a type discipline to guarantee the soundness of reduction rules with respect…
The essence of sequential recommender systems (RecSys) lies in understanding how users make decisions. Most existing approaches frame the task as sequential prediction based on users' historical purchase records. While effective in…
We present a sequent calculus for first-order logic with lambda terms and definite descriptions. The theory formalised by this calculus is essentially Russellian, but avoids some of its well known drawbacks and treats definite description…
We develop a general criterion for cut elimination in sequent calculi for propositional modal logics, which rests on absorption of cut, contraction, weakening and inversion by the purely modal part of the rule system. Our criterion applies…
This work presents a reduced order modelling technique built on a high fidelity embedded mesh finite element method. Such methods, and in particular the CutFEM method, are attractive in the generation of projection-based reduced order…
Logic is the science of correct inferences and a logical system is a tool to prove assertions in a certain logic in a correct way. There are many logical systems, and many ways of formalizing them, e.g., using natural deduction or sequent…
The CUR decomposition is a technique for low-rank approximation that selects small subsets of the columns and rows of a given matrix to use as bases for its column and rowspaces. It has recently attracted much interest, as it has several…
Intensional sets, i.e., sets given by a property rather than by enumerating elements, are widely recognized as a key feature to describe complex problems (see, e.g., specification languages such as B and Z). Notwithstanding, very few tools…