Abstract argumentation frameworks (AFs) provide the basis for various reasoning problems in the area of Artificial Intelligence. Efficient evaluation of AFs has thus been identified as an important research challenge. So far, implemented systems for evaluating AFs have either followed a straight-forward reduction-based approach or been limited to certain tractable classes of AFs. In this work, we present a generic approach for reasoning over AFs, based on the novel concept of complexity-sensitivity. Establishing the theoretical foundations of this approach, we derive several new complexity results for preferred, semi-stable and stage semantics which complement the current complexity landscape for abstract argumentation, providing further understanding on the sources of intractability of AF reasoning problems. The introduced generic framework exploits decision procedures for problems of lower complexity whenever possible. This allows, in particular, instantiations of the generic framework via harnessing in an iterative way current sophisticated Boolean satisfiability (SAT) solver technology for solving the considered AF reasoning problems. First experimental results show that the SAT-based instantiation of our novel approach outperforms existing systems.

In predicate invention (PI), new predicates are introduced into a logical theory, usually by rewriting a group of closely-related rules to use a common invented predicate as a "subroutine". PI is difficult, since a poorly-chosen invented predicate may lead to error cascades. Here we suggest a "soft" version of predicate invention: instead of explicitly creating new predicates, we implicitly group closely-related rules by using structured sparsity to regularize their parameters together. We show that soft PI, unlike hard PI, consistently improves over previous strong baselines for structure-learning on two large-scale tasks.

This paper revisits the problem of learning a k-CNF Boolean function from examples, for fixed k, in the context of online learning under the logarithmic loss. We give a Bayesian interpretation to one of Valiant’s classic PAC learning algorithms, which we then build upon to derive three efficient, online, probabilistic, supervised learning algorithms for predicting the output of an unknown k-CNF Boolean function. We analyze the loss of our methods, and show that the cumulative log-loss can be upper bounded by a polynomial function of the size of each example.

Most logic-based machine learning algorithms rely on an Occamist bias where textual complexity of hypotheses is minimised. Within Inductive Logic Programming (ILP), this approach fails to distinguish between the efficiencies of hypothesised programs, such as quick sort (O(n log n)) and bubble sort (O(n 2 )). This paper addresses this issue by considering techniques to minimise both the textual complexity and resource complexity of hypothesised robot strategies. We develop a general framework for the problem of minimising resource complexity and show that on two robot strategy problems, 1) Postman 2) Sorter (recursively sort letters for delivery), the theoretical resource complexities of optimal strategies vary depending on whether objects can be composed within a strategy. The approach considered is an extension of Meta-Interpretive Learning (MIL), a recently developed paradigm in ILP which supports predicate invention and the learning of recursive logic programs. We introduce a new MIL implementation, Metagol O , and prove its convergence, with increasing numbers of randomly chosen examples to optimal strategies of this kind. Our experiments show that Metagol O learns theoretically optimal robot sorting strategies, which is in agreement with the theoretical predictions showing a clear divergence in resource requirements as the number of objects grows. To the authors’ knowledge this paper is the first demonstration of a learning algorithm able to learn optimal resource complexity robot strategies and algorithms for sorting lists.

Classic entrenchment-based contraction is not applicable to many useful logics, such as description logics. This is because the semantic construction refers to arbitrary disjunctions of formulas, while many logics do not fully support disjunction. In this paper, we present a new entrenchment-based contraction which does not rely on any logical connectives except conjunction. This contraction is applicable to all fragments of first-order logic that support conjunction. We provide a representation theorem for the contraction which shows that it satisfies all the AGM postulates except for the controversial Recovery Postulate, and is a natural generalisation of entrenchment-based contraction.

In this paper, we study the expressive power of first-order disjunctive logic programming (DLP) and normal logic programming (NLP) under the stable model semantics. We show that, unlike the propositional case, first-order DLP is strictly more expressive than NLP. This result still holds even if auxiliary predicates are allowed, assuming that NP not equals to coNP. On the other side, we propose a partial translation from first-order DLP to NLP via unfolding and shifting, which suggests a sound yet incomplete approach to implement DLP via NLP solvers. We also identify some NLP definable subclasses, and conjecture to exactly capture NLP definability by unfolding and shifting.

We consider a simple language for writing causal action theories, and postulate several properties for the state transition models of these theories. We then consider some possible embeddings of these causal action theories in some other action formalisms, and their implementations in logic programs with answer set semantics. In particular, we propose to consider what we call permissible translations from these causal action theories to logic programs. We identify two sets of properties, and prove that for each set, there is only one permissible translation, under strong equivalence, that can satisfy all properties in the set. As it turns out, for one set, the unique permissible translation is essentially the same as Balduccini and Gelfond's translation from Gelfond and Lifschitz's action language B to logic programs. For the other, it is essentially the same as Lifschitz and Turner's translation from the action language C to logic programs. This work provides a new perspective on understanding, evaluating and comparing action languages by using sets of properties instead of examples. It will be interesting to see if other action languages can be similarly characterized, and whether new action formalisms can be defined using different sets of properties.

A knowledge-based program defines the behavior of an agent by combining primitive actions, programming constructs and test conditions that make explicit reference to the agent's knowledge. In this paper we consider a setting where an agent is equipped with a Description Logic (DL) knowledge base providing general domain knowledge and an incomplete description of the initial situation. We introduce a corresponding new DL-based action language that allows for representing both physical and sensing actions, and that we then use to build knowledge-based programs with test conditions expressed in the epistemic DL. After proving undecidability for the general case, we then discuss a restricted fragment where verification becomes decidable. The provided proof is constructive and comes with an upper bound on the procedure's complexity.

Preference Inference involves inferring additional user preferences from elicited or observed preferences, based on assumptions regarding the form of the user's preference relation. In this paper we consider a situation in which alternatives have an associated vector of costs, each component corresponding to a different criterion, and are compared using a kind of lexicographic order, similar to the way alternatives are compared in a Hierarchical Constraint Logic Programming model. It is assumed that the user has some (unknown) importance ordering on criteria, and that to compare two alternatives, firstly, the combined cost of each alternative with respect to the most important criteria are compared; only if these combined costs are equal, are the next most important criteria considered. The preference inference problem then consists of determining whether a preference statement can be inferred from a set of input preferences. We show that this problem is co-NP-complete, even if one restricts the cardinality of the equal-importance sets to have at most two elements, and one only considers non-strict preferences. However, it is polynomial if it is assumed that the user's ordering of criteria is a total ordering; it is also polynomial if the sets of equally important criteria are all equivalence classes of a given fixed equivalence relation. We give an efficient polynomial algorithm for these cases, which also throws light on the structure of the inference.

Fundamental to reasoning about actions and beliefs is the projection problem: to decide what is believed after a sequence of actions is performed. Progression is one widely applied technique to solve this problem. In this paper we propose a novel framework for computing progression in the epistemic situation calculus. In particular, we model an agent's preferential belief structure using conditional statements and provide a technique for updating these conditional statements as actions are performed and sensing information is received. Moreover, we show, by using the concepts of natural revision and only-believing, that the progression of a conditional knowledge base can be represented by only-believing the revised set of conditional statements. These results lay the foundations for feasible belief progression due to the unique-model property of only-believing.