Dichotomies in Ontology-Mediated Querying with the Guarded Fragment

We study the complexity of ontology-mediated querying when ontologies are formulated in the guarded fragment of first-order logic (GF). Our general aim is to classify the data complexity on the level of ontologies where query evaluation w.r.t. an ontology O is considered to be in PTime if all (unions of conjunctive) queries can be evaluated in PTime w.r.t. O and coNP-hard if at least one query is coNP-hard w.r.t. O. We identify several large and relevant fragments of GF that enjoy a dichotomy between PTime and coNP, some of them additionally admitting a form of counting. In fact, almost all ontologies in the BioPortal repository fall into these fragments or can easily be rewritten to do so. We then establish a variation of Ladner's Theorem on the existence of NP-intermediate problems and use this result to show that for other fragments, there is provably no such dichotomy. Again for other fragments (such as full GF), establishing a dichotomy implies the Feder-Vardi conjecture on the complexity of constraint satisfaction problems. We also link these results to Datalog-rewritability and study the decidability of whether a given ontology enjoys PTime query evaluation, presenting both positive and negative results

Model Comparison Games for Horn Description Logics

Horn description logics are syntactically defined fragments of standard description logics that fall within the Horn fragment of first-order logic and for which ontology-mediated query answering is in PTime for data complexity. They were independently introduced in modal logic to capture the intersection of Horn first-order logic with modal logic. In this paper, we introduce model comparison games for the basic Horn description logic hornALC (corresponding to the basic Horn modal logic) and use them to obtain an Ehrenfeucht-Fra\"iss\'e type definability result and a van Benthem style expressive completeness result for hornALC. We also establish a finite model theory version of the latter. The Ehrenfeucht-Fra\"iss\'e type definability result is used to show that checking hornALC indistinguishability of models is ExpTime-complete, which is in sharp contrast to ALC indistinguishability (i.e., bisimulation equivalence) checkable in PTime. In addition, we explore the behavior of Horn fragments of more expressive description and modal logics by defining a Horn guarded fragment of first-order logic and introducing model comparison games for it

Minimal model reasoning for modal logic

Model generation and minimal model generation are useful for tasks such as model checking, query answering and for debugging of logical specifications. Due to this variety of applications, several minimality criteria and model generation methods for classical logics have been studied. Minimal model generation for modal logics however did not receive the same attention from the research community. This thesis aims to fill this gap by investigating minimality criteria and designing minimal model generation procedures for all the sublogics of the multi-modal logic S5(m) and their extensions with universal modalities. All the procedures are minimal model sound and complete, in the sense that they generate all and only minimal models. The starting point of the investigation is the definition of a Herbrand semantics for modal logics on which a syntactic minimality criterion is devised. The syntactic nature of the minimality criterion allows for an efficient minimal model generation procedure, but, on the other hand, the resulting minimal models can be redundant or semantically non minimal with respect to each other. To overcome the syntactic limitations of the first minimality criterion, the thesis moves from minimal modal Herbrand models to semantic minimality criteria based on subset-simulation. At first, theoretical procedures for the generation of models minimal modulo subset-simulation are presented. These procedures for the generation of models minimal modulo subset-simulation are minimal model sound and complete, but they might not terminate. The minimality criterion and the procedures are then refined in such a way that termination can be ensured while preserving minimal model soundness and completeness

Minimal Model Reasoning for Modal Logic

Model generation and minimal model generation are useful for tasks such as model checking, query answering and for debugging of logical specifications. Due to this variety of applications, several minimality criteria and model generation methods for classical logics have been studied. Minimal model generation for modal logics however did not receive the same attention from the research community. This thesis aims to fill this gap by investigating minimality criteria and designing minimal model generation procedures for all the sublogics of the multi-modal logic S5(m) and their extensions with universal modalities. All the procedures are minimal model sound and complete, in the sense that they generate all and only minimal models. The starting point of the investigation is the definition of a Herbrand semantics for modal logics on which a syntactic minimality criterion is devised. The syntactic nature of the minimality criterion allows for an efficient minimal model generation procedure, but, on the other hand, the resulting minimal models can be redundant or semantically non minimal with respect to each other. To overcome the syntactic limitations of the first minimality criterion, the thesis moves from minimal modal Herbrand models to semantic minimality criteria based on subset-simulation. At first, theoretical procedures for the generation of models minimal modulo subset-simulation are presented. These procedures for the generation of models minimal modulo subset-simulation are minimal model sound and complete, but they might not terminate. The minimality criterion and the procedures are then refined in such a way that termination can be ensured while preserving minimal model soundness and completeness

StreamB: {A} Declarative Language for Automatically Processing Data Streams in Abstract Environments for Agent Platforms

none2noneAngelo Ferrando; Fabio PapacchiniFerrando, Angelo; Papacchini, Fabi

StreamB:A Declarative Language for Automatically Processing Data Streams in Abstract Environments for Agent Platforms

To apply BDI agents to real-world scenarios, the reality-gap, between the low-level data (perceptions) and their high-level representation (beliefs), must be bridged. This is usually achieved by a manual mapping. There are two problems with this solution: (i) if the environment changes, the mapping has to be changed as well (by the developer); (ii) part of the mapping might end up being implemented at the agent level increasing the code complexity and reducing its generality. In this paper, we present a general approach to automate the mapping between low-level data and high-level beliefs through the use of transducers. These transducers gather information from the environment and map them to high-level beliefs according to formal temporal specifications. We present our technique and we show its applicability through a case study involving the remote inspection of a nuclear plant

Computing Minimal Models Modulo Subset-Simulation for Modal Logics

In this paper we propose a novel minimality criterion for models of modal logics based on a variation of the notion of simulation, called subset-simulation. We present a minimal model sound and complete tableau calculus for the generation of this new kind of minimal models for the multi-modal logic K (m), and we discuss extensions to cover more expressive logics. The generation of minimal models is performed incrementally by using a minimality test to close branches representing non-minimal models, or to update the set of minimal models. Subset-simulation minimal models have the advantage that they are semantically more natural than models obtained by using syntactic minimality criteria