Base revision in classical logic is done by the removal of formulas. Exploiting the non-monotonicity of ASP allows one to propose other revision strategies, namely addition strategy or removal and/or addition strategy. These strategies allow one to define families of rule-based revision operators. The paper presents a semantic characterization of these families of revision operators in terms of answer sets. This semantic characterization allows for equivalently considering the evolution of syntactic logic programs and the evolution of their semantic content. It then studies the logical properties of the proposed operators and gives complexity results.

One of the key advantages of Inductive Logic Programming systems is the ability of the domain experts to provide background knowledge as modes that allow for efficient search through the space of hypotheses. However, there is an inherent assumption that this expert should also be an ILP expert to provide effective modes. We relax this assumption by designing a graphical user interface that allows the domain expert to interact with the system using Entity Relationship diagrams. These interactions are used to construct modes for the learning system. We evaluate our algorithm on a probabilistic logic learning system where we demonstrate that the user is able to construct effective background knowledge on par with the expert-encoded knowledge on five data sets.

We consider the problem of learning generalized first-order representations of concepts from a single example. To address this challenging problem, we augment an inductive logic programming learner with two novel algorithmic contributions. First, we define a distance measure between candidate concept representations that improves the efficiency of search for target concept and generalization. Second, we leverage richer human inputs in the form of advice to improve the sample-efficiency of learning. We prove that the proposed distance measure is semantically valid and use that to derive a P AC bound. Our experimental analysis on diverse concept learning tasks demonstrates both the effectiveness and efficiency of the proposed approach over a first-order concept learner using only examples.

This paper proposes a tentative and original survey of meeting points between Knowledge Representation and Reasoning (KRR) and Machine Learning (ML), two areas which have been developing quite separately in the last three decades. Some common concerns are identified and discussed such as the types of used representation, the roles of knowledge and data, the lack or the excess of information, or the need for explanations and causal understanding. Then some methodologies combining reasoning and learning are reviewed (such as inductive logic programming, neuro-symbolic reasoning, formal concept analysis, rule-based representations and ML, uncertainty in ML, or case-based reasoning and analogical reasoning), before discussing examples of synergies between KRR and ML (including topics such as belief functions on regression, EM algorithm versus revision, the semantic description of vector representations, the combination of deep learning with high level inference, knowledge graph completion, declarative frameworks for data mining, or preferences and recommendation). This paper is the first step of a work in progress aiming at a better mutual understanding of research in KRR and ML, and how they could cooperate.

Humans engage in informal debates on a daily basis. By expressing their opinions and ideas in an argumentative fashion, they are able to gain a deeper understanding of a given problem and in some cases, find the best possible course of actions towards resolving it. In this paper, we develop a methodology to verify debates formalised as abstract argumentation frameworks. We first present a translation from debates to transition systems. Such transition systems can model debates and represent their evolution over time using a finite set of states. We then formalise relevant debate properties using temporal and strategy logics. These formalisations, along with a debate transition system, allow us to verify whether a given debate satisfies certain properties. The verification process can be automated using model checkers. Therefore, we also measure their performance when verifying debates, and use the results to discuss the feasibility of model checking debates.

In this paper, we investigate a bitopological duality for algebras of Fitting's multi-valued logic. We also extend the natural duality theory for ISP I( L) by developing a duality for ISP(L), where L is a finite algebra in which underlying lattice is bounded distributive. Keywords: Bitopology, Fitting's logic, Natural duality theory. 1 Introduction Stone's pioneering work in the mid 1930 [19] on the dual equivalence between the category of Boolean algebras and homomorphism, and the category of Stone spaces(compact zero-dimensional Hausdorff spaces) and continuous maps, is being considered as the origin of duality theory. Stone further developed a general work [12] for the category of bounded distributive lattices in 1937. Priestley in 1970 [18] investigate another duality for the category of bounded distributive lattices with the help of ordered Stone spaces(known as Priesley spaces), which overcome difficulties in Stone's work [12].

In multi-agent domains (MADs), an agent's action may not just change the world and the agent's knowledge and beliefs about the world, but also may change other agents' knowledge and beliefs about the world and their knowledge and beliefs about other agents' knowledge and beliefs about the world. The goals of an agent in a multi-agent world may involve manipulating the knowledge and beliefs of other agents' and again, not just their knowledge/belief about the world, but also their knowledge about other agents' knowledge about the world. Our goal is to present an action language (mA+) that has the necessary features to address the above aspects in representing and RAC in MADs. mA+ allows the representation of and reasoning about different types of actions that an agent can perform in a domain where many other agents might be present -- such as world-altering actions, sensing actions, and announcement/communication actions. It also allows the specification of agents' dynamic awareness of action occurrences which has future implications on what agents' know about the world and other agents' knowledge about the world. mA+ considers three different types of awareness: full-, partial- awareness, and complete oblivion of an action occurrence and its effects. This keeps the language simple, yet powerful enough to address a large variety of knowledge manipulation scenarios in MADs. The semantics of mA+ relies on the notion of state, which is described by a pointed Kripke model and is used to encode the agent's knowledge and the real state of the world. It is defined by a transition function that maps pairs of actions and states into sets of states. We illustrate properties of the action theories, including properties that guarantee finiteness of the set of initial states and their practical implementability. Finally, we relate mA+ to other related formalisms that contribute to RAC in MADs.

LTLf synthesis is the automated construction of a reactive system from a high-level description, expressed in LTLf, of its finite-horizon behavior. So far, the conversion of LTLf formulas to deterministic finite-state automata (DFAs) has been identified as the primary bottleneck to the scalabity of synthesis. Recent investigations have also shown that the size of the DFA state space plays a critical role in synthesis as well. Therefore, effective resolution of the bottleneck for synthesis requires the conversion to be time and memory performant, and prevent state-space explosion. Current conversion approaches, however, which are based either on explicit-state representation or symbolic-state representation, fail to address these necessities adequately at scale: Explicit-state approaches generate minimal DFA but are slow due to expensive DFA minimization. Symbolic-state representations can be succinct, but due to the lack of DFA minimization they generate such large state spaces that even their symbolic representations cannot compensate for the blow-up. This work proposes a hybrid representation approach for the conversion. Our approach utilizes both explicit and symbolic representations of the state-space, and effectively leverages their complementary strengths. In doing so, we offer an LTLf to DFA conversion technique that addresses all three necessities, hence resolving the bottleneck. A comprehensive empirical evaluation on conversion and synthesis benchmarks supports the merits of our hybrid approach.

Powerful formalisms for abstract argumentation have been proposed, among them abstract dialectical frameworks (ADFs) that allow for a succinct and flexible specification of the relationship between arguments, and the GRAPPA framework which allows argumentation scenarios to be represented as arbitrary edge-labelled graphs. The complexity of ADFs and GRAPPA is located beyond NP and ranges up to the third level of the polynomial hierarchy. The combined complexity of Answer Set Programming (ASP) exactly matches this complexity when programs are restricted to predicates of bounded arity. In this paper, we exploit this coincidence and present novel efficient translations from ADFs and GRAPPA to ASP. More specifically, we provide reductions for the five main ADF semantics of admissible, complete, preferred, grounded, and stable interpretations, and exemplify how these reductions need to be adapted for GRAPPA for the admissible, complete and preferred semantics. Under consideration in Theory and Practice of Logic Programming (TPLP).

One of the most difficult tasks in higher-order theorem proving is the instantiation of set variables [ 2, 3 ]. An important class of theorem proving problems requiring instantia tion of a set variable are those requiring induction [ 5 ]. Instantiating a set variable often requires synthesizing a formula satisfying some properties. In our work we apply machine le arning to the task of synthesizing formulas satisfying a collection of semantic properties . Previous work applying machine learning to induction theorem proving can be found in [ 7 ].