Related papers: On the Trap Space Semantics of Normal Logic Progra…
Recent work on neuro-symbolic inductive logic programming has led to promising approaches that can learn explanatory rules from noisy, real-world data. While some proposals approximate logical operators with differentiable operators from…
Differentiable logics (DL) have recently been proposed as a method of training neural networks to satisfy logical specifications. A DL consists of a syntax in which specifications are stated and an interpretation function that translates…
One approach to explaining the hierarchical levels of understanding within a machine learning model is the symbolic method of inductive logic programming (ILP), which is data efficient and capable of learning first-order logic rules that…
Abductive logic programs offer a formalism to declaratively represent and reason about problems in a variety of areas: diagnosis, decision making, hypothetical reasoning, etc. On the other hand, logic program updates allow us to express…
Neural-symbolic integration aims to combine the connectionist subsymbolic with the logical symbolic approach to artificial intelligence. In this paper, we first define the answer set semantics of (boolean) neural nets and then introduce…
On the Semantic Web, metadata and ontologies are used to enable computers to read data. The Web Ontology Language (OWL) has been proposed as a standard ontological language, and various inference systems for this language have been studied.…
This paper proposes a structural and dynamical framework for modeling cognitive processes within a cybernetic perspective. Cognitive states are represented as elements of a state space evolving through an iterative update rule of the form…
The regular models of a normal logic program are a particular type of partial (i.e. 3-valued) models which correspond to stable partial models with minimal undefinedness. In this paper, we explore graphical conditions on the dependency…
Answer Set Programming (ASP) is logic programming under the stable model or answer set semantics. During the last decade, this paradigm has seen several extensions by generalizing the notion of atom used in these programs. Among these,…
Current high-performance semantic segmentation models are purely data-driven sub-symbolic approaches and blind to the structured nature of the visual world. This is in stark contrast to human cognition which abstracts visual perceptions at…
In this paper we systematically investigate the connections between logics with a finite number of variables, structures of bounded pathwidth, and linear Datalog Programs. We prove that, in the context of Constraint Satisfaction Problems,…
Abductive logic programming offers a formalism to declaratively express and solve problems in areas such as diagnosis, planning, belief revision and hypothetical reasoning. Tabled logic programming offers a computational mechanism that…
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…
This paper presents an example of formal reasoning about the semantics of a Prolog program of practical importance (the SAT solver of Howe and King). The program is treated as a definite clause logic program with added control. The logic…
We examine the meaning and the complexity of probabilistic logic programs that consist of a set of rules and a set of independent probabilistic facts (that is, programs based on Sato's distribution semantics). We focus on two semantics,…
Current open-domain neural semantics parsers show impressive performance. However, closer inspection of the symbolic meaning representations they produce reveals significant weaknesses: sometimes they tend to merely copy character sequences…
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…
In this paper we provide a unifying description of different types of semantics of modal logic found in the literature via the framework of topological categories. In the style of categorical logic, we establish an exact correspondence…
Epistemic logic programs constitute an extension of the stable models semantics to deal with new constructs called subjective literals. Informally speaking, a subjective literal allows checking whether some regular literal is true in all…
Neural networks can be regarded as a new programming paradigm, i.e., instead of building ever-more complex programs through (often informal) logical reasoning in the programmers' mind, complex 'AI' systems are built by optimising generic…