Abstract Team Semantics is a generalization of Tarskian Semantics in which formulas are satisfied with respect to sets of assignments, called teams. In this semantics, it is possible to add new atoms and connectives expressing dependencies between possible values of variables. Some of the resulting logics are more expressive than first-order logic while others are not. I study the (relativizable) atoms and families of atoms that do not increase the expressive power of first-order logic when they and their complements are added to it, separately or jointly, calling them doubly strongly first-order dependencies and finding a characterization for them.

Perceptron operators have been introduced to knowledge representation languages such as description logics in order to define concepts by listing features with associated weights and by giving a threshold. Semantically, an individual then belongs to such a concept if the weighted sum of the listed features it belongs to reaches that threshold. Such operators have been subsequently applied to cognitively-motivated modelling scenarios and to building bridges between learning and reasoning. However, they suffer from the basic limitation that they cannot consider the weight or number of role fillers. This paper introduces an extension of the basic perceptron operator language to address this shortcoming, defining the language ALCP and answering some basic questions regarding the succinctness and complexity of the new language. Namely, we show firstly that in ALCP+, when weights are positive, the language is expressively equivalent to ALCQ, whilst it is strictly more expressive in the general case allowing also negative weights. Secondly, ALCP+ is shown to be strictly more succinct than ALCQ. Thirdly, capitalising on results concerning the logic ALCSCC, we show that despite the added expressivity, reasoning in ALCP remains EXPTIME-complete.

When considering two concepts in terms of extensional logic, their combination will often be trivial, returning an empty extension. Consider e.g. “a Fish Vehicle”, i.e., “a Vehicle which is also a Fish”. Still, people use sophisticated strategies to produce new, non-empty concepts. All these strategies involve the human ability to mend the conflicting attributes of the input concepts and to create new properties of the combination. We focus in particular on the case where a Head concept has superior ‘asymmetric’ control over steering the resulting combination (or hybridisation) with a Modifier concept. Specifically, we propose a dialogical model of the cognitive and logical mechanics of this asymmetric form of hybridisation. Its implementation is then evaluated using a combination of example ontologies.

Causal team semantics ([2]) supports causal-observational languages, which enrich the languages for deterministic causation ([11], [18]) with dependencies and other team-specific operators. Handling the causal aspects of these languages requires a richer semantics than propositional team semantics; nonetheless, in this paper we show that the causal-observational languages considered in [2] can be embedded into first-order dependence logic by means of a translation and a careful choice of models. We show that, in some significant cases, the translation can be refined to an embedding into the Bernays-Schönfinkel-Ramsey fragment of dependence logic or, in the restricted case of recursive causal models, into the existential fragment. As an application, we use the embeddings to show the decidability of a satisfiability problem for the causal-observational languages. Along the way, we question the correctness of the semantics for interventionist counterfactuals proposed by Halpern ([18]) and propose an alternative one which behaves as usual in the uncontroversial recursive case.

When people combine concepts these are often characterised as “hybrid”, “impossible”, or “humorous”. However, when simply considering them in terms of extensional logic, the novel concepts understood as a conjunctive concept will often lack meaning having an empty extension (consider “a tooth that is a chair”, “a pet flower”, etc.). Still, people use different strategies to produce new non-empty concepts: additive or integrative combination of features, alignment of features, instantiation, etc. All these strategies involve the ability to deal with conflicting attributes and the creation of new (combinations of) properties. We here consider in particular the case where a Head concept has superior ‘asymmetric’ control over steering the resulting concept combination (or hybridisation) with a Modifier concept. Specifically, we propose a dialogical approach to concept combination and discuss an implementation based on axiom weakening, which models the cognitive and logical mechanics of this asymmetric form of hybridisation.

Abstract In Team Semantics, a dependency notion is strongly first order if every sentence of the logic obtained by adding the corresponding atoms to First-Order Logic is equivalent to some first-order sentence. In this work it is shown that all nontrivial dependency atoms that are strongly first order, downwards closed, and relativizable (in the sense that the relativizations of the corresponding atoms with respect to some unary predicate are expressible in terms of them) are definable in terms of constancy atoms. Additionally, it is shown that any strongly first-order dependency is safe for any family of downwards closed dependencies, in the sense that every sentence of the logic obtained by adding to First-Order Logic both the strongly first-order dependency and the downwards closed dependencies is equivalent to some sentence of the logic obtained by adding only the downwards closed dependencies.

Ontology engineering is a hard and error-prone task, in which small changes may lead to errors, or even produce an inconsistent ontology. As ontologies grow in size, the need for automated methods for repairing inconsistencies while preserving as much of the original knowledge as possible increases. Most previous approaches to this task are based on removing a few axioms from the ontology to regain consistency. We propose a new method based on weakening these axioms to make them less restrictive, employing the use of refinement operators. We introduce the theoretical framework for weakening DL ontologies, propose algorithms to repair ontologies based on the framework, and provide an analysis of the computational complexity. Through an empirical analysis made over real-life ontologies, we show that our approach preserves significantly more of the original knowledge of the ontology than removing axioms.

Axiom weakening is a novel technique that allows for fine-grained repair of inconsistent ontologies. In a multi-agent setting, integrating ontologies corresponding to multiple agents may lead to inconsistencies. Such inconsistencies can be resolved after the integrated ontology has been built, or their generation can be prevented during ontology generation. We implement and compare these two approaches. First, we study how to repair an inconsistent ontology resulting from a voting-based aggregation of views of heterogeneous agents. Second, we prevent the generation of inconsistencies by letting the agents engage in a turn-based rational protocol about the axioms to be added to the integrated ontology. We instantiate the two approaches using real-world ontologies and compare them by measuring the levels of satisfaction of the agents w.r.t. the ontology obtained by the two procedures.

We develop an automated variational inference method for Bayesian structured prediction problems with Gaussian process (GP) priors and linear-chain likelihoods. Our approach does not need to know the details of the structured likelihood model and can scale up to a large number of observations. Furthermore, we show that the required expected likelihood term and its gradients in the variational objective (ELBO) can be estimated efficiently by using expectations over very low-dimensional Gaussian distributions. Optimization of the ELBO is fully parallelizable over sequences and amenable to stochastic optimization, which we use along with control variate techniques to make our framework useful in practice. Results on a set of natural language processing tasks show that our method can be as good as (and sometimes better than, in particular with respect to expected log-likelihood) hard-coded approaches including SVM-struct and CRF, and overcomes the scalability limitations of previous inference algorithms based on sampling. Overall, this is a fundamental step to developing automated inference methods for Bayesian structured prediction.

We investigate the properties of Inclusion Logic, that is, First Order Logic with Team Semantics extended with inclusion dependencies. We prove that Inclusion Logic is equivalent to Greatest Fixed Point Logic, and we prove that all union-closed first-order definable properties of relations are definable in it. We also provide an Ehrenfeucht-Fraïssé game for Inclusion Logic, and give an example illustrating its use.

We study the expressive power of fragments of inclusion and independence logic defined either by restricting the number of universal quantifiers or the arity of inclusion and independence atoms in formulas. Assuming the so-called lax semantics for these logics, we relate these fragments of inclusion and independence logic to familiar sublogics of existential second-order logic. We also show that, with respect to the stronger strict semantics, inclusion logic is equivalent to existential second-order logic.