相关论文: Ordering-based Representations of Rational Inferen…

We combine Recurrent Neural Networks with Tensor Product Representations to learn combinatorial representations of sequential data. This improves symbolic interpretation and systematic generalisation. Our architecture is trained end-to-end…

A mathematical model of Subject behaviour choice is proposed. The background of the model is the concept of two preference relations determining Subject behaviour. These are an "internal" or subjective preference relation and an "external"…

Relative belief inferences are shown to arise as Bayes rules or limiting Bayes rules. These inferences are invariant under reparameterizations and possess a number of optimal properties. In particular, relative belief inferences are based…

A famous result due to Ko and Friedman (1982) asserts that the problems of integration and maximisation of a univariate real function are computationally hard in a well-defined sense. Yet, both functionals are routinely computed at great…

We present a modification of the superposition calculus that is meant to generate consequences of sets of first-order axioms. This approach is proven to be sound and deductive-complete in the presence of redundancy elimination rules,…

In relational approach to general rough sets, ideas of directed relations are supplemented with additional conditions for multiple algebraic approaches in this research paper. The relations are also specialized to representations of general…

A recent flurry of research activity has attempted to quantitatively define "fairness" for decisions based on statistical and machine learning (ML) predictions. The rapid growth of this new field has led to wildly inconsistent terminology…

Developed by Buchberger for commutative polynomial rings, Groebner Bases are frequently applied to solve algorithmic problems, such as the congruence problem for ideals. Until now, these ideas have been transmitted to different in part…

Current end-to-end semantic role labeling is mostly accomplished via graph-based neural models. However, these all are first-order models, where each decision for detecting any predicate-argument pair is made in isolation with local…

When allowing concurrent actions in Markov Decision Processes, whose state and action spaces grow exponentially in the number of objects, computing a policy becomes highly inefficient, as it requires enumerating the joint of the two spaces.…

I have argued elsewhere that second order logic provides a foundation for mathematics much in the same way as set theory does, despite the fact that the former is second order and the latter first order, but second order logic is marred by…

In this paper, we give two proofs of the wellfoundedness of recursive notation systems for $\Pi_N$-reflecting ordinals. One is based on $\Pi_{N-1}^0$-inductive definitions, and the other is based on distinguished classes.

First-order logic with dependent sorts, such as Makkai's first-order logic with dependent sorts (FOLDS), or Aczel's and Belo's dependently typed (intuitionistic) first-order logic (DFOL), may be regarded as logic enriched dependent type…

Across machine learning (ML) sub-disciplines, researchers make explicit mathematical assumptions in order to facilitate proof-writing. We note that, specifically in the area of fairness-accuracy trade-off optimization scholarship, similar…

We introduce information bearing systems (IBRS) as an abstraction of many logical systems. We define a general semantics for IBRS, and show that IBRS generalize in a natural way preferential semantics and solve open representation problems.

Notions of k-asimulation and asimulation are introduced as asymmetric counterparts to k-bisimulation and bisimulation, respectively. It is proved that a first-order formula is equivalent to a standard translation of an intuitionistic…

When teaching an elementary logic course to students who have a general scientific background but have never been exposed to logic, we have to face the problem that the notions of deduction rule and of derivation are completely new to them,…

Reference analysis produces objective Bayesian inference, in the sense that inferential statements depend only on the assumed model and the available data, and the prior distribution used to make an inference is least informative in a…

This paper discusses the processes by which conversants in a dialogue can infer whether their assertions and proposals have been accepted or rejected by their conversational partners. It expands on previous work by showing that logical…

We demonstrate the first Recurrent Neural Network architecture for learning Signal Temporal Logic formulas, and present the first systematic comparison of formula inference methods. Legacy systems embed much expert knowledge which is not…