15 found
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  1.  41
    Inclusion and Exclusion Dependencies in Team Semantics—on Some Logics of Imperfect Information.Pietro Galliani - 2012 - Annals of Pure and Applied Logic 163 (1):68-84.
  2.  29
    Perceptron Connectives in Knowledge Representation.Pietro Galliani, Guendalina Righetti, Daniele Porello, Oliver Kutz & Nicolas Toquard - 2020 - In Knowledge Engineering and Knowledge Management - 22nd International Conference, {EKAW} 2020, Bolzano, Italy, September 16-20, 2020, Proceedings. Lecture Notes in Computer Science 12387. pp. 183-193.
    We discuss the role of perceptron (or threshold) connectives in the context of Description Logic, and in particular their possible use as a bridge between statistical learning of models from data and logical reasoning over knowledge bases. We prove that such connectives can be added to the language of most forms of Description Logic without increasing the complexity of the corresponding inference problem. We show, with a practical example over the Gene Ontology, how even simple instances of perceptron connectives are (...)
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  3.  38
    Asymmetric Hybrids: Dialogues for Computational Concept Combination.Guendalina Righetti, Daniele Porello, Nicolas Troquard, Oliver Kutz, Maria Hedblom & Pietro Galliani - 2022 - In Fabian Neuhaus & Boyan Brodaric (eds.), Formal Ontology in Information Systems - Proceedings of the Twelfth International Conference, {FOIS} 2021, Bozen-Bolzano, Italy, September 11-18, 2021. Frontiers in Artificial Intelligence and Applications. IOS Press. pp. 81-96.
    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 (...)
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  4. Two Approaches to Ontology Aggregation Based on Axiom Weakening.Daniele Porello, Nicolaas Troquard, Oliver Kutz, Rafael Penaloza, Roberto Confalonieri & Pietro Galliani - 2018 - In Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence, {IJCAI} 2018, July 13-19, 2018, Stockholm, Sweden. pp. 1942--1948.
    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 (...)
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  5.  61
    Epistemic Operators in Dependence Logic.Pietro Galliani - 2013 - Studia Logica 101 (2):367-397.
    The properties of the ${\forall^{1}}$ quantifier defined by Kontinen and Väänänen in [13] are studied, and its definition is generalized to that of a family of quantifiers ${\forall^{n}}$ . Furthermore, some epistemic operators δ n for Dependence Logic are also introduced, and the relationship between these ${\forall^{n}}$ quantifiers and the δ n operators are investigated.The Game Theoretic Semantics for Dependence Logic and the corresponding Ehrenfeucht- Fraissé game are then adapted to these new connectives.Finally, it is proved that the ${\forall^{1}}$ quantifier (...)
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  6.  94
    A Toothful of Concepts: Towards a Theory of Weighted Concept Combination.Daniele Porello, Oliver Kutz, Guendalina Righetti, Nicolas Troquard, Pietro Galliani & Claudio Masolo - 2019 - In Mantas Simkus & Grant E. Weddell (eds.), Proceedings of the 32nd International Workshop on Description Logics, Oslo, Norway, June 18-21, 2019.
    We introduce a family of operators to combine Description Logic concepts. They aim to characterise complex concepts that apply to instances that satisfy \enough" of the concept descriptions given. For instance, an individual might not have any tusks, but still be considered an elephant. To formalise the meaning of "enough", the operators take a list of weighted concepts as arguments, and a certain threshold to be met. We commence a study of the formal properties of these operators, and study some (...)
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  7.  31
    Towards Knowledge-Driven Distillation and Explanation of Black-Box Models.Roberto Confalonieri, Guendalina Righetti, Pietro Galliani, Nicolas Toquard, Oliver Kutz & Daniele Porello - 2021 - In Proceedings of the Workshop on Data meets Applied Ontologies in Explainable {AI} {(DAO-XAI} 2021) part of Bratislava Knowledge September {(BAKS} 2021), Bratislava, Slovakia, September 18th to 19th, 2021. CEUR 2998.
    We introduce and discuss a knowledge-driven distillation approach to explaining black-box models by means of two kinds of interpretable models. The first is perceptron (or threshold) connectives, which enrich knowledge representation languages such as Description Logics with linear operators that serve as a bridge between statistical learning and logical reasoning. The second is Trepan Reloaded, an ap- proach that builds post-hoc explanations of black-box classifiers in the form of decision trees enhanced by domain knowledge. Our aim is, firstly, to target (...)
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  8.  21
    General Models and Entailment Semantics for Independence Logic.Pietro Galliani - 2013 - Notre Dame Journal of Formal Logic 54 (2):253-275.
    We develop a semantics for independence logic with respect to what we will call general models. We then introduce a simpler entailment semantics for the same logic, and we reduce the validity problem in the former to the validity problem in the latter. Then we build a proof system for independence logic and prove its soundness and completeness with respect to entailment semantics.
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  9.  46
    The Dynamification of Modal Dependence Logic.Pietro Galliani - 2013 - Journal of Logic, Language and Information 22 (3):269-295.
    We examine the transitions between sets of possible worlds described by the compositional semantics of Modal Dependence Logic, and we use them as the basis for a dynamic version of this logic. We give a game theoretic semantics, a (compositional) transition semantics and a power game semantics for this new variant of modal Dependence Logic, and we prove their equivalence; and furthermore, we examine a few of the properties of this formalism and show that Modal Dependence Logic can be recovered (...)
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  10.  21
    Repairing Socially Aggregated Ontologies Using Axiom Weakening.Daniele Porello, Nicolas Triquard, Roberto Confalonieri, Pietro Galliani, Oliver Kutz & Rafael Penaloza - 2017 - In {PRIMA} 2017: Principles and Practice of Multi-Agent Systems - 20th International Conference, Nice, France, October 30 - November 3, 2017, Proceedings. Lecture Notes in Computer Science 10621,. pp. 441-449.
    Ontologies represent principled, formalised descriptions of agents’ conceptualisations of a domain. For a community of agents, these descriptions may differ among agents. We propose an aggregative view of the integration of ontologies based on Judgement Aggregation (JA). Agents may vote on statements of the ontologies, and we aim at constructing a collective, integrated ontology, that reflects the individual conceptualisations as much as possible. As several results in JA show, many attractive and widely used aggregation procedures are prone to return inconsistent (...)
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  11.  67
    Lottery Semantics: A Compositional Semantics for Probabilistic First-Order Logic with Imperfect Information.Pietro Galliani & Allen L. Mann - 2013 - Studia Logica 101 (2):293-322.
    We present a compositional semantics for first-order logic with imperfect information that is equivalent to Sevenster and Sandu’s equilibrium semantics (under which the truth value of a sentence in a finite model is equal to the minimax value of its semantic game). Our semantics is a generalization of an earlier semantics developed by the first author that was based on behavioral strategies, rather than mixed strategies.
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  12.  10
    Towards Even More Irresistible Axiom Weakening.Roberto Confalonieri, Pietro Galliani, Oliver Kutz, Daniele Porello, Guendalina Righetti & Nicolas Toquard - 2020 - In Proceedings of the 33rd International Workshop on Description Logics {(DL} 2020) co-located with the 17th International Conference on Principles of Knowledge Representation and Reasoning {(KR} 2020), Online Event, Rhodes, Greece.
    Axiom weakening is a technique that allows for a fine-grained repair of inconsistent ontologies. Its main advantage is that it repairs on- tologies by making axioms less restrictive rather than by deleting them, employing the use of refinement operators. In this paper, we build on pre- viously introduced axiom weakening for ALC, and make it much more irresistible by extending its definitions to deal with SROIQ, the expressive and decidable description logic underlying OWL 2 DL. We extend the definitions of (...)
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  13.  1
    Embedding Causal Team Languages Into Predicate Logic.Fausto Barbero & Pietro Galliani - forthcoming - Annals of Pure and Applied Logic:103159.
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  14.  6
    Characterizing Downwards Closed, Strongly First-Order, Relativizable Dependencies.Pietro Galliani - 2019 - Journal of Symbolic Logic 84 (3):1136-1167.
    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 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 (...)
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  15.  1
    The Doxastic Interpretation of Team Semantics. [REVIEW]Pietro Galliani - 2015 - In Andrés Villaveces, Roman Kossak, Juha Kontinen & Åsa Hirvonen (eds.), Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics. De Gruyter. pp. 167-192.
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