Related papers: SCL(FOL) Revisited
For polar codes, successive cancellation list (SCL) decoding algorithm significantly improves finite-length performance compared to SC decoding. SCL-flip decoding can further enhance the performance but the gain diminishes as code length…
In this paper, a new calculus on sequences is defined. Also, the $\lambda$-derivative and the $\lambda$-integration are investigated. The fundamental theorem of $\lambda$-calculus is included. A suitable function basis for the…
Abstract. Matching logic cannot handle concurrency. We introduce concurrent matching logic (CML) to reason about fault-free partial correctness of shared-memory concurrent programs. We also present a soundness proof for concurrent matching…
In this paper, we introduce two focussed sequent calculi, LKp(T) and LK+(T), that are based on Miller-Liang's LKF system for polarised classical logic. The novelty is that those sequent calculi integrate the possibility to call a decision…
A logic calculus is presented that is a conservative extension of linear logic. The motivation beneath this work concerns lazy evaluation, true concurrency and interferences in proof search. The calculus includes two new connectives to deal…
We introduce a natural Turing-complete extension of first-order logic FO. The extension adds two novel features to FO. The first one of these is the capacity to add new points to models and new tuples to relations. The second one is the…
Prior work in semantic parsing has shown that conventional seq2seq models fail at compositional generalization tasks. This limitation led to a resurgence of methods that model alignments between sentences and their corresponding meaning…
Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to…
Continual Learning (CL) focuses on learning from dynamic and changing data distributions while retaining previously acquired knowledge. Various methods have been developed to address the challenge of catastrophic forgetting, including…
Cut-elimination is the bedrock of proof theory. It is the algorithm that eliminates cuts from a sequent calculus proof that leads to cut-free calculi and applications. Cut-elimination applies to many logics irrespective of their semantics.…
We study the logic FO(~), the extension of first-order logic with team semantics by unrestricted Boolean negation. It was recently shown axiomatizable, but otherwise has not yet received much attention in questions of computational…
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 provide a novel computer-assisted technique for systematically analyzing first-order methods for optimization. In contrast with previous works, the approach is particularly suited for handling sublinear convergence rates and stochastic…
The goal of Continual Learning (CL) task is to continuously learn multiple new tasks sequentially while achieving a balance between the plasticity and stability of new and old knowledge. This paper analyzes that this insufficiency arises…
We study the problem of explainability-first clustering where explainability becomes a first-class citizen for clustering. Previous clustering approaches use decision trees for explanation, but only after the clustering is completed. In…
Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in the…
There are two competing paradigms in successful SAT solvers: Conflict-driven clause learning (CDCL) and stochastic local search (SLS). CDCL uses systematic exploration of the search space and has the ability to learn new clauses. SLS…
Distributed First Order Logic (DFOL) has been introduced more than ten years ago with the purpose of formalising distributed knowledge-based systems, where knowledge about heterogeneous domains is scattered into a set of interconnected…
Temporal Equilibrium Logic (TEL) is a promising framework that extends the knowledge representation and reasoning capabilities of Answer Set Programming with temporal operators in the style of LTL. To our knowledge it is the first…
Model theoretic results such as Characterization and Definability give important information about different logics. It is well known that the proofs of those results for several modal logics have, somehow, the same 'taste'. A general proof…