scholarly journals A Logic For Decidable Reasoning About Actions

2021 ◽  
Author(s):  
Yilan Gu ◽  
Mikhail Soutchanski
Keyword(s):  
Description Logic ◽  
Description Logics ◽  
Order Logic ◽  
Situation Calculus ◽  
Semantic Web Services ◽  
Reasoning About Actions ◽  
First Order ◽  
Projection Problem ◽  
Initial Knowledge ◽  
Taxonomic Reasoning

We consider a modified version of the situation calculus built using a two-variable fragment of the first-order logic extended with counting quantifiers. We mention several additional groups of axioms that can be introduced to capture taxonomic reasoning. We show that the regression operator in this framework can be defined similarly to regression in Reiter’s version of the situation calculus. Using this new regression operator, we show that the projection and executability problems (the important reasoning tasks in the situation calculus) are decidable in the modified version even if an initial knowledge base is incomplete. We also discuss the complexity of solving the projection problem in this modified language in general. Furthermore, we define description logic based sub-languages of our modified situation calculus. They are based on the description logics ALCO(U) (or ALCQO(U), respectively). We show that in these sub-languages solving the projection problem has better computational complexity than in the general modified situation calculus. We mention possible applications to formalization of Semantic Web services and some connections with reasoning about actions based on description logics.

scholarly journals A Logic For Decidable Reasoning About Actions

2021 ◽  
Author(s):  
Yilan Gu ◽  
Mikhail Soutchanski
Keyword(s):  
Description Logic ◽  
Description Logics ◽  
Order Logic ◽  
Situation Calculus ◽  
Semantic Web Services ◽  
Reasoning About Actions ◽  
First Order ◽  
Projection Problem ◽  
Initial Knowledge ◽  
Taxonomic Reasoning

We consider a modified version of the situation calculus built using a two-variable fragment of the first-order logic extended with counting quantifiers. We mention several additional groups of axioms that can be introduced to capture taxonomic reasoning. We show that the regression operator in this framework can be defined similarly to regression in Reiter’s version of the situation calculus. Using this new regression operator, we show that the projection and executability problems (the important reasoning tasks in the situation calculus) are decidable in the modified version even if an initial knowledge base is incomplete. We also discuss the complexity of solving the projection problem in this modified language in general. Furthermore, we define description logic based sub-languages of our modified situation calculus. They are based on the description logics ALCO(U) (or ALCQO(U), respectively). We show that in these sub-languages solving the projection problem has better computational complexity than in the general modified situation calculus. We mention possible applications to formalization of Semantic Web services and some connections with reasoning about actions based on description logics.

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 Towards an Expressive Practical Logical Action Theory

10.29007/2m22 ◽  
2018 ◽  
Author(s):  
Mikhail Soutchanski ◽  
Wael Yehia
Keyword(s):  
Description Logic ◽  
Action Theory ◽  
Broad Class ◽  
Situation Calculus ◽  
Logical Formula ◽  
Local Effects ◽  
Seamless Integration ◽  
Reasoning About Actions ◽  
Projection Problem ◽  
Action Theories

In the area of reasoning about actions, one of the key computational problems is the projection problem: to find whether a given logical formula is true afterperforming a sequence of actions. This problem is undecidable in the generalsituation calculus; however, it is decidable in some fragments. We considera fragment P of the situation calculus and Reiter's basic action theories (BAT)such that the projection problem can be reduced to the satisfiability problemin an expressive description logic $ALCO(U)$ that includes nominals ($O$),the universal role ($U$), and constructs from the well-known logic $ALC$. It turns outthat our fragment P is more expressive than previously explored description logicbased fragments of the situation calculus. We explore some of the logical properties of our theories.In particular, we show that the projection problem can be solved using regressionin the case where BATs include a general ``static" TBox, i.e., an ontology that hasno occurrences of fluents. Thus, we propose seamless integration of traditionalontologies with reasoning about actions. We also show that the projectionproblem can be solved using progression if all actions have only local effects onthe fluents, i.e., in P, if one starts with an incomplete initial theory thatcan be transformed into an $ALCO(U)$ concept, then its progression resulting fromexecution of a ground action can still be expressed in the same language. Moreover,we show that for a broad class of incomplete initial theories progression can be computed efficiently.

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.

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.

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 Worst-Case Optimal Querying of Very Expressive Description Logics with Path Expressions and Succinct Counting

2019 ◽  
Author(s):  
Bartosz Bednarczyk ◽  
Sebastian Rudolph
Keyword(s):  
Description Logics ◽  
Order Logic ◽  
Conjunctive Query ◽  
Cardinality Constraints ◽  
Worst Case ◽  
First Order ◽  
Regular Path ◽  
Regular Path Queries ◽  
Carry Over ◽  
Path Queries

Among the most expressive knowledge representation formalisms are the description logics of the Z family. For well-behaved fragments of ZOIQ, entailment of positive two-way regular path queries is well known to be 2EXPTIME-complete under the proviso of unary encoding of numbers in cardinality constraints. We show that this assumption can be dropped without an increase in complexity and EXPTIME-completeness can be achieved when bounding the number of query atoms, using a novel reduction from query entailment to knowledge base satisfiability. These findings allow to strengthen other results regarding query entailment and query containment problems in very expressive description logics. Our results also carry over to GC2, the two-variable guarded fragment of first-order logic with counting quantifiers, for which hitherto only conjunctive query entailment has been investigated.

scholarly journals Probabilistic Description Logics for Subjective Uncertainty

2017 ◽  
Vol 58 ◽  
pp. 1-66 ◽  
Author(s):  
Victor Gutierrez-Basulto ◽  
Jean Christoph Jung ◽  
Carsten Lutz ◽  
Lutz Schröder
Keyword(s):  
Description Logics ◽  
Order Logic ◽  
First Order Logic ◽  
Two Dimensional ◽  
Subjective Probabilities ◽  
Subjective Uncertainty ◽  
First Order ◽  
New Family ◽  
Probabilistic Description

We propose a family of probabilistic description logics (DLs) that are derived in a principled way from Halpern's probabilistic first-order logic. The resulting probabilistic DLs have a two-dimensional semantics similar to temporal DLs and are well-suited for representing subjective probabilities. We carry out a detailed study of reasoning in the new family of logics, concentrating on probabilistic extensions of the DLs ALC and EL, and showing that the complexity ranges from PTime via ExpTime and 2ExpTime to undecidable.

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