Related papers: The Logic of Logic Programming
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…
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…
Convincing someone of the truth value of a premise requires understanding and articulating the core logical structure of the argument which proves or disproves the premise. Understanding the logical structure of an argument refers to…
We propose a method to adapt functional logic programming to deal with reasoning on coinductively interpreted programs as well as on inductively interpreted programs. In order to do so, we consider a class of objects interesting for this…
Splitting a logic program allows us to reduce the task of computing its stable models to similar tasks for its subprograms. This can be used to increase solving performance and prove program correctness. We generalize the conditions under…
Logic program transformation by the unfold/fold method ad- vocates the writing of correct logic programs via the application of some rules to a naive program. This work focuses on how to overcome subgoal- introduction difficulties in…
Inductive logic programming (ILP) is a form of logic-based machine learning. The goal is to induce a hypothesis (a logic program) that generalises given training examples. As ILP turns 30, we review the last decade of research. We focus on…
We discuss proving correctness and completeness of definite clause logic programs. We propose a method for proving completeness, while for proving correctness we employ a method which should be well known but is often neglected. Also, we…
Equilibrium logic is an approach to nonmonotonic reasoning that extends the stable-model and answer-set semantics for logic programs. In particular, it includes the general case of nested logic programs, where arbitrary Boolean combinations…
This extended abstract gives a brief outline of the connections between the descriptions and variable concepts. Thus, the notion of a concept is extended to include both the syntax and semantics features. The evaluation map in use is…
Completeness of a logic program means that the program produces all the answers required by its specification. The cut is an important construct of programming language Prolog. It prunes part of the search space, this may result in a loss…
Modal logic is a paradigm for several useful and applicable formal systems in computer science. It generally retains the low complexity of classical propositional logic, but notable exceptions exist in the domains of description, temporal,…
We show how categorial deduction can be implemented in higher-order (linear) logic programming, thereby realising parsing as deduction for the associative and non-associative Lambek calculi. This provides a method of solution to the parsing…
The limit behavior of inductive logic programs has not been explored, but when considering incremental or online inductive learning algorithms which usually run ongoingly, such behavior of the programs should be taken into account. An…
Transparency is a key requirement for ethical machines. Verified ethical behavior is not enough to establish justified trust in autonomous intelligent agents: it needs to be supported by the ability to explain decisions. Logic Programming…
Based on an analysis of the inference rules used, we provide a characterization of the situations in which classical provability entails intuitionistic provability. We then examine the relationship of these derivability notions to uniform…
Logic programming has developed as a rich field, built over a logical substratum whose main constituent is a nonclassical form of negation, sometimes coexisting with classical negation. The field has seen the advent of a number of…
This paper presents a soundness and completeness proof for propositional intuitionistic calculus with respect to the semantics of computability logic. The latter interprets formulas as interactive computational problems, formalized as games…
The main contribution of the present paper is the introduction of a simple yet expressive hybrid-dynamic logic for describing quantum programs. This version of quantum logic can express quantum measurements and unitary evolutions of states…
Inductive logic programming (ILP) is a form of logical machine learning. The goal is to search a hypothesis space for a hypothesis that generalises training examples and background knowledge. We introduce an approach that 'shrinks' the…