Related papers: Restricted Predicates for Hypothetical Datalog
By representing words with probability densities rather than point vectors, probabilistic word embeddings can capture rich and interpretable semantic information and uncertainty. The uncertainty information can be particularly meaningful in…
This report defines (plain) Dag-like derivations in the purely implicational fragment of minimal logic $M_{\supset}$. Introduce the horizontal collapsing set of rules and the algorithm {\bf HC}. Explain why {\bf HC} can transform any…
While knowledge representation and reasoning are considered the keys for human-level artificial intelligence, connectionist networks have been shown successful in a broad range of applications due to their capacity for robust learning and…
Mathematical proof aims to deliver confident conclusions, but a very similar process of deduction can be used to make uncertain estimates that are open to revision. A key ingredient in such reasoning is the use of a "default" estimate of…
In this work, we show that both logic programming and abstract argumentation frameworks can be interpreted in terms of Nelson's constructive logic N4. We do so by formalizing, in this logic, two principles that we call non-contradictory…
This paper maps out the relation between different approaches for handling preferences in argumentation with strict rules and defeasible assumptions by offering translations between them. The systems we compare are: non-prioritized defeats…
A very desirable Datalog extension investigated by many researchers in the last thirty years consists in allowing the use of the basic SQL aggregates min, max, count and sum in recursive rules. In this paper, we propose a simple…
Relational data in its most basic form is a static collection of known facts. However, by learning to infer and deduct additional information and structure, we can massively increase the usefulness of the underlying data. One common form of…
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 consider the problem of implementing deontic modal logic. We show how (deontic) modal operators can be elegantly and directly expressed using default negation (negation-as-failure) and strong negation present in answer set programming…
We extend the $ASPIC^+$ framework for structured argumentation so as to allow applications of the reasoning by cases inference scheme for defeasible arguments. Given an argument with conclusion `$A$ or $B$', an argument based on $A$ with…
We develop a model of abduction in abstract argumentation, where changes to an argumentation framework act as hypotheses to explain the support of an observation. We present dialogical proof theories for the main decision problems (i.e.,…
Probabilistic extensions of logic programming languages, such as ProbLog, integrate logical reasoning with probabilistic inference to evaluate probabilities of output relations; however, prior work does not account for potential statistical…
This paper presents a logical approach to nonmonotonic reasoning based on the notion of a nonmonotonic consequence relation. A conditional knowledge base, consisting of a set of conditional assertions of the type "if ... then ...",…
As an ubiquitous method in natural language processing, word embeddings are extensively employed to map semantic properties of words into a dense vector representation. They capture semantic and syntactic relations among words but the…
We propose a deep learning-based approach to the problem of premise selection: selecting mathematical statements relevant for proving a given conjecture. We represent a higher-order logic formula as a graph that is invariant to variable…
Deep and shallow embeddings of non-classical logics in classical higher-order logic have been explored, implemented, and used in various reasoning tools in recent years. This paper presents a method for the simultaneous deployment of deep…
Implicit deep learning prediction rules generalize the recursive rules of feedforward neural networks. Such rules are based on the solution of a fixed-point equation involving a single vector of hidden features, which is thus only…
Implicit arguments, which cannot be detected solely through syntactic cues, make it harder to extract predicate-argument tuples. We present a new model for implicit argument prediction that draws on reading comprehension, casting the…
Defeasible logics provide several linguistic features to support the expression of defeasible knowledge. There is also a wide variety of such logics, expressing different intuitions about defeasible reasoning. However, the logics can only…