Related papers: Foundations of regular coinduction
Regularization of neural machine translation is still a significant problem, especially in low-resource settings. To mollify this problem, we propose regressing word embeddings (ReWE) as a new regularization technique in a system that is…
Regularization is a core component of modern inverse problems, as it helps establish the well-posedness of the solution of interest. Popular regularization approaches include variational regularization and iterative regularization. The…
The form and justification of inductive inference rules depend strongly on the representation of uncertainty. This paper examines one generic representation, namely, incomplete information. The notion can be formalized by presuming that the…
Induction is the process by which we obtain predictive laws or theories or models of the world. We consider the structural aspect of induction. We answer the question as to whether we can find a finite and minmalistic set of operations on…
We define an inference system to capture explanations based on causal statements, using an ontology in the form of an IS-A hierarchy. We first introduce a simple logical language which makes it possible to express that a fact causes another…
Coreference resolution is essential for natural language understanding and has been long studied in NLP. In recent years, as the format of Question Answering (QA) became a standard for machine reading comprehension (MRC), there have been…
Language technologies that accurately model the dynamics of events must perform commonsense reasoning. Existing work evaluating commonsense reasoning focuses on making inferences about common, everyday situations. To instead investigate the…
Rule-based reasoning, a fundamental type of legal reasoning, enables us to draw conclusions by accurately applying a rule to a set of facts. We explore causal language models as rule-based reasoners, specifically with respect to…
Decision analysis deals with modeling and enhancing decision processes. A principal challenge in improving behavior is in obtaining a transparent description of existing behavior in the first place. In this paper, we develop an expressive,…
Inference is the process of using facts we know to learn about facts we do not know. A theory of inference gives assumptions necessary to get from the former to the latter, along with a definition for and summary of the resulting…
Formal deductive systems are very common in computer science. They are used to represent logics, programming languages, and security systems. Moreover, writing programs that manipulate them and that reason about them is important and…
We study causal inference in a multi-environment setting, in which the functional relations for producing the variables from their direct causes remain the same across environments, while the distribution of exogenous noises may vary. We…
Humans and animals exhibit a range of interesting behaviors in dynamic environments, and it is unclear how our brains actively reformat this dense sensory information to enable these behaviors. Experimental neuroscience is undergoing a…
We introduce a generalized logic programming paradigm where programs, consisting of facts and rules with the usual syntax, can be enriched by co-facts, which syntactically resemble facts but have a special meaning. As in coinductive logic…
We extend to natural deduction the approach of Linear Nested Sequents and of 2-sequents. Formulas are decorated with a spatial coordinate, which allows a formulation of formal systems in the original spirit of natural deduction -- only one…
Deduction is the one of the major forms of inferences and commonly used in formal logic. This kind of inference has the feature of monotonicity, which can be problematic. There are different types of inferences that are not monotonic, e.g.…
A {\it dynamic reasoning system} (DRS) is an adaptation of a conventional formal logical system that explicitly portrays reasoning as a temporal activity, with each extralogical input to the system and each inference rule application being…
We introduce provenance networks, a novel class of neural models designed to provide end-to-end, training-data-driven explainability. Unlike conventional post-hoc methods, provenance networks learn to link each prediction directly to its…
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…
An inductive theorem proving method for constrained term rewriting systems, which is based on rewriting induction, needs a decision procedure for reduction-completeness of constrained terms. In addition, the sufficient complete property of…