Related papers: Restricted Predicates for Hypothetical Datalog
The dynamics of belief and knowledge is one of the major components of any autonomous system that should be able to incorporate new pieces of information. We introduced the Horn knowledge base dynamics to deal with two important points:…
In this paper we propose a framework for combining Disjunctive Logic Programming and Poole's Probabilistic Horn Abduction. We use the concept of hypothesis to specify the probability structure. We consider the case in which probabilistic…
In functional programming, datatypes a la carte provide a convenient modular representation of recursive datatypes, based on their initial algebra semantics. Unfortunately it is highly challenging to implement this technique in proof…
In this paper we explore a unifying approach --- that of hypotheses assumption --- as a means to provide a semantics for all Normal Logic Programs (NLPs), the Minimal Hypotheses (MH) semantics. This semantics takes a positive hypotheses…
With widening deployments of natural language processing (NLP) in daily life, inherited social biases from NLP models have become more severe and problematic. Previous studies have shown that word embeddings trained on human-generated…
Abstract predicates are considered in this paper as abstraction technique for heap-separated configurations, and as genuine Prolog predicates which are translated straight into a corresponding formal language grammar used as validation…
With help of a compact Prolog-based theorem prover for Intuitionistic Propositional Logic, we synthesize minimal assumptions under which a given formula formula becomes a theorem. After applying our synthesis algorithm to cover basic…
Traditional neural embeddings represent concepts as points, excelling at similarity but struggling with higher-level reasoning and asymmetric relationships. We introduce a novel paradigm: embedding concepts as linear subspaces. This…
The aim of the present paper is to show that the concept of intuitionistic logic based on a Heyting algebra can be generalized in such a way that it is formalized by means of a bounded poset. In this case it is not assumed that the poset is…
We propose an efficient interpretable neuro-symbolic model to solve Inductive Logic Programming (ILP) problems. In this model, which is built from a set of meta-rules organised in a hierarchical structure, first-order rules are invented by…
This paper introduces epistemic graphs as a generalization of the epistemic approach to probabilistic argumentation. In these graphs, an argument can be believed or disbelieved up to a given degree, thus providing a more fine--grained…
A general framework is proposed for integration of rules and external first order theories. It is based on the well-founded semantics of normal logic programs and inspired by ideas of Constraint Logic Programming (CLP) and constructive…
Ontology embeddings map classes, roles, and individuals in ontologies into $\mathbb{R}^n$, and within $\mathbb{R}^n$ similarity between entities can be computed or new axioms inferred. For ontologies in the Description Logic…
In this paper we present a transformation of finite propositional default theories into so-called propositional argumentation systems. This transformation allows to characterize all notions of Reiter's default logic in the framework of…
The paper presents a constraint based semantic formalism for HPSG. The syntax-semantics interface directly implements syntactic conditions on quantifier scoping and distributivity. The construction of semantic representations is guided by…
A correspondence is established between the elements of logic reasoning systems (knowledge bases, rules, inference and queries) and the hardware and dynamical operations of neural networks. The correspondence is framed as a general…
In this paper, we provide more evidence for the contention that logical consequence should be understood in normative terms. Hartry Field and John MacFarlane covered the classical case. We extend their work, examining what it means for an…
We report on the mechanization of (preference-based) conditional normative reasoning. Our focus is on Aqvist's system E for conditional obligation, and its extensions. Our mechanization is achieved via a shallow semantical embedding in…
Knowledge bases are employed in a variety of applications from natural language processing to semantic web search; alas, in practice their usefulness is hurt by their incompleteness. Embedding models attain state-of-the-art accuracy in…
The development of logic has largely been through the 'deductive' paradigm: conclusions are inferred from established premisses. However, the use of logic in the context of both human and machine reasoning is typically through the dual…