scholarly journals Using formal ontology for the representation of morphological properties of anatomical structures in endoscopic surgery

2020 ◽  
Vol 6 (1) ◽  
Author(s):  
Ralph Schäfermeier ◽  
Alexandr Uciteli ◽  
Stefan Kropf ◽  
Heinrich Herre
Keyword(s):  
Endoscopic Surgery ◽  
Description Logic ◽  
Order Logic ◽  
First Order Logic ◽  
Morphological Properties ◽  
Formal Ontology ◽  
Anatomical Structures ◽  
Landmark Recognition ◽  
First Order ◽  
Formal Framework

AbstractIn this paper we present results to the problem of an adequate and compact symbolic representation of morphological features of anatomical structures that serve as surgical landmarks for automated assistance in endoscopic surgery using the General Formal Ontology (GFO) as a formal framework. For this purpose, we employed a translation from this first-order logic representation to a more compact description logic based formalism with the associated benefits, such as the availability of decidable reasoning procedures, for the purpose of automated landmark recognition in a hybrid symbolic/subsymbolic AI approach.

scholarly journals Ontology-Mediated Querying with the Description Logic EL: Trichotomy and Linear Datalog Rewritability

2017 ◽  
Author(s):  
Carsten Lutz ◽  
Leif Sabellek
Keyword(s):  
Description Logic ◽  
Order Logic ◽  
First Order Logic ◽  
Data Complexity ◽  
First Order ◽  
Fine Grained ◽  
Linear Recursion

We consider ontology-mediated queries (OMQs) based on an EL ontology and an atomic query (AQ), provide an ultimately fine-grained analysis of data complexity and study rewritability into linear Datalog-aiming to capture linear recursion in SQL. Our main results are that every such OMQ is in AC0, NL-complete or PTime-complete, and that containment in NL coincides with rewritability into linear Datalog (whereas containment in AC0 coincides with rewritability into first-order logic). We establish natural characterizations of the three cases, show that deciding linear Datalog rewritability (as well as the mentioned complexities) is ExpTime-complete, give a way to construct linear Datalog rewritings when they exist, and prove that there is no constant bound on the arity of IDB relations in linear Datalog rewritings.

Logics for the Semantic Web

2011 ◽  
pp. 24-43
Author(s):  
J. Bruijn
Keyword(s):  
Semantic Web ◽  
Logic Programming ◽  
Description Logic ◽  
Description Logics ◽  
Order Logic ◽  
First Order Logic ◽  
Horn Logic ◽  
First Order ◽  
Logical Language ◽  
Rule Languages

This chapter introduces a number of formal logical languages which form the backbone of the Semantic Web. They are used for the representation of both ontologies and rules. The basis for all languages presented in this chapter is the classical first-order logic. Description logics is a family of languages which represent subsets of first-order logic. Expressive description logic languages form the basis for popular ontology languages on the Semantic Web. Logic programming is based on a subset of first-order logic, namely Horn logic, but uses a slightly different semantics and can be extended with non-monotonic negation. Many Semantic Web reasoners are based on logic programming principles and rule languages for the Semantic Web based on logic programming are an ongoing discussion. Frame Logic allows object-oriented style (frame-based) modeling in a logical language. RuleML is an XML-based syntax consisting of different sublanguages for the exchange of specifications in different logical languages over the Web.

scholarly journals A Characterization Theorem for a Modal Description Logic

2017 ◽  
Author(s):  
Paul Wild ◽  
Lutz Schröder
Keyword(s):  
Description Logic ◽  
Description Logics ◽  
Characterization Theorem ◽  
Expressive Power ◽  
Order Logic ◽  
First Order Logic ◽  
Standard Description ◽  
First Order ◽  
Information State ◽  
Modal Description

Modal description logics feature modalities that capture dependence of knowledge on parameters such as time, place, or the information state of agents. E.g., the logic S5-ALC combines the standard description logic ALC with an S5-modality that can be understood as an epistemic operator or as representing (undirected) change. This logic embeds into a corresponding modal first-order logic S5-FOL. We prove a modal characterization theorem for this embedding, in analogy to results by van Benthem and Rosen relating ALC to standard first-order logic: We show that S5-ALC with only local roles is, both over finite and over unrestricted models, precisely the bisimulation-invariant fragment of S5-FOL, thus giving an exact description of the expressive power of S5-ALC with only local roles.

scholarly journals A Modal Characterization Theorem for a Probabilistic Fuzzy Description Logic

2019 ◽  
Author(s):  
Paul Wild ◽  
Lutz Schröder ◽  
Dirk Pattinson ◽  
Barbara König
Keyword(s):  
Description Logic ◽  
Characterization Theorem ◽  
Expressive Power ◽  
Order Logic ◽  
First Order Logic ◽  
First Order ◽  
Type Spaces ◽  
Suitable Notion ◽  
Fuzzy Description

The fuzzy modality probably is interpreted over probabilistic type spaces by taking expected truth values. The arising probabilistic fuzzy description logic is invariant under probabilistic bisimilarity; more informatively, it is non-expansive wrt. a suitable notion of behavioural distance. In the present paper, we provide a characterization of the expressive power of this logic based on this observation: We prove a probabilistic analogue of the classical van Benthem theorem, which states that modal logic is precisely the bisimulation-invariant fragment of first-order logic. Specifically, we show that every formula in probabilistic fuzzy first-order logic that is non-expansive wrt. behavioural distance can be approximated by concepts of bounded rank in probabilistic fuzzy description logic.

scholarly journals Logical Separability of Incomplete Data under Ontologies

2020 ◽  
Author(s):  
Jean Christoph Jung ◽  
Carsten Lutz ◽  
Hadrien Pulcini ◽  
Frank Wolter
Keyword(s):  
Incomplete Data ◽  
Decision Problem ◽  
Description Logic ◽  
Order Logic ◽  
First Order Logic ◽  
Logical Formula ◽  
Database Queries ◽  
First Order ◽  
Ontology Language ◽  
Guarded Fragment

Finding a logical formula that separates positive and negative examples given in the form of labeled data items is fundamental in applications such as concept learning, reverse engineering of database queries, and generating referring expressions. In this paper, we investigate the existence of a separating formula for incomplete data in the presence of an ontology. Both for the ontology language and the separation language, we concentrate on first-order logic and three important fragments thereof: the description logic ALCI, the guarded fragment, and the two-variable fragment. We consider several forms of separability that differ in the treatment of negative examples and in whether or not they admit the use of additional helper symbols to achieve separation. We characterize separability in a model-theoretic way, compare the separating power of the different languages, and determine the computational complexity of separability as a decision problem.

scholarly journals Exact Query Reformulation over Databases with First-order and Description Logics Ontologies

2013 ◽  
Vol 48 ◽  
pp. 885-922 ◽  
Author(s):  
E. Franconi ◽  
V. Kerhet ◽  
N. Ngo
Keyword(s):  
General Framework ◽  
Description Logic ◽  
Description Logics ◽  
Effective Means ◽  
Order Logic ◽  
First Order Logic ◽  
Query Rewriting ◽  
Query Reformulation ◽  
First Order ◽  
Sql Query

We study a general framework for query rewriting in the presence of an arbitrary first-order logic ontology over a database signature. The framework supports deciding the existence of a safe-range first-order equivalent reformulation of a query in terms of the database signature, and if so, it provides an effective approach to construct the reformulation based on interpolation using standard theorem proving techniques (e.g., tableau). Since the reformulation is a safe-range formula, it is effectively executable as an SQL query. At the end, we present a non-trivial application of the framework with ontologies in the very expressive ALCHOIQ description logic, by providing effective means to compute safe-range first-order exact reformulations of queries.

First-Order Logic Reasoning Support for the Semantic Web

2009 ◽  
Vol 19 (12) ◽  
pp. 3091-3099 ◽  
Author(s):  
Gui-Hong XU ◽  
Jian ZHANG
Keyword(s):  
Semantic Web ◽  
Order Logic ◽  
First Order Logic ◽  
First Order ◽  
Logic Reasoning

Boolean-valued structures

2018 ◽  
Author(s):  
Tim Button ◽  
Sean Walsh
Keyword(s):  
Model Theory ◽  
Order Logic ◽  
First Order Logic ◽  
Inference Rules ◽  
Mathematical Concepts ◽  
Semantic Framework ◽  
First Order ◽  
Standard Models ◽  
Boolean Valued Model ◽  
Semantic Values

Chapters 6-12 are driven by questions about the ability to pin down mathematical entities and to articulate mathematical concepts. This chapter is driven by similar questions about the ability to pin down the semantic frameworks of language. It transpires that there are not just non-standard models, but non-standard ways of doing model theory itself. In more detail: whilst we normally outline a two-valued semantics which makes sentences True or False in a model, the inference rules for first-order logic are compatible with a four-valued semantics; or a semantics with countably many values; or what-have-you. The appropriate level of generality here is that of a Boolean-valued model, which we introduce. And the plurality of possible semantic values gives rise to perhaps the ‘deepest’ level of indeterminacy questions: How can humans pin down the semantic framework for their languages? We consider three different ways for inferentialists to respond to this question.

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