On the expressive power of modal logics on trees

1992 ◽  
pp. 441-451 ◽  
Author(s):  
Bernd-Holger Schlingloff
Keyword(s):  
Expressive Power ◽  
Modal Logics

scholarly journals Pooling Modalities and Pointwise Intersection: Semantics, Expressivity, and Dynamics

2022 ◽  
Author(s):  
Frederik Van De Putte ◽  
Dominik Klein
Keyword(s):  
Expressive Power ◽  
Modal Logics ◽  
Relational Semantics ◽  
Modal Operators

AbstractWe study classical modal logics with pooling modalities, i.e. unary modal operators that allow one to express properties of sets obtained by the pointwise intersection of neighbourhoods. We discuss salient properties of these modalities, situate the logics in the broader area of modal logics (with a particular focus on relational semantics), establish key properties concerning their expressive power, discuss dynamic extensions of these logics and provide reduction axioms for the latter.

scholarly journals THE EXPRESSIVE POWER OF MEMORY LOGICS

2011 ◽  
Vol 4 (2) ◽  
pp. 290-318 ◽  
Author(s):  
CARLOS ARECES ◽  
DIEGO FIGUEIRA ◽  
SANTIAGO FIGUEIRA ◽  
SERGIO MERA
Keyword(s):  
Modal Logic ◽  
Expressive Power ◽  
Modal Logics ◽  
Hybrid Logic ◽  
Satisfiability Problem ◽  
Current Node

We investigate the expressive power of memory logics. These are modal logics extended with the possibility to store (or remove) the current node of evaluation in (or from) a memory, and to perform membership tests on the current memory. From this perspective, the hybrid logic ℋℒ (↓), for example, can be thought of as a particular case of a memory logic where the memory is an indexed list of elements of the domain.This work focuses in the case where the memory is a set, and we can test whether the current node belongs to the set or not. We prove that, in terms of expressive power, the memory logics we discuss here lie between the basic modal logic ${\cal K}$ and ℋℒ (↓). We show that the satisfiability problem of most of the logics we cover is undecidable. The only logic with a decidable satisfiability problem is obtained by imposing strong constraints on which elements can be memorized.

A Modal Defeasible Reasoner of Deontic Logic for the Semantic Web

2011 ◽  
Vol 7 (1) ◽  
pp. 18-43 ◽  
Author(s):  
Efstratios Kontopoulos ◽  
Nick Bassiliades ◽  
Guido Governatori ◽  
Grigoris Antoniou
Keyword(s):  
Modal Logic ◽  
Semantic Web ◽  
Deontic Logic ◽  
Expressive Power ◽  
Modal Logics ◽  
Cognitive State ◽  
Privacy Requirements ◽  
Defeasible Logic ◽  
Conflicting Information ◽  
Web Information

Defeasible logic is a non-monotonic formalism that deals with incomplete and conflicting information, whereas modal logic deals with the concepts of necessity and possibility. These types of logics play a significant role in the emerging Semantic Web, which enriches the available Web information with meaning, leading to better cooperation between end-users and applications. Defeasible and modal logics, in general, and, particularly, deontic logic provide means for modeling agent communities, where each agent is characterized by its cognitive profile and normative system, as well as policies, which define privacy requirements, access permissions, and individual rights. Toward this direction, this article discusses the extension of DR-DEVICE, a Semantic Web-aware defeasible reasoner, with a mechanism for expressing modal logic operators, while testing the implementation via deontic logic operators, concerned with obligations, permissions, and related concepts. The motivation behind this work is to develop a practical defeasible reasoner for the Semantic Web that takes advantage of the expressive power offered by modal logics, accompanied by the flexibility to define diverse agent behaviours. A further incentive is to study the various motivational notions of deontic logic and discuss the cognitive state of agents, as well as the interactions among them.

A Modal Defeasible Reasoner of Deontic Logic for the Semantic Web

Semantic Web ◽  
2013 ◽  
pp. 140-167
Author(s):  
Efstratios Kontopoulos ◽  
Nick Bassiliades ◽  
Guido Governatori ◽  
Grigoris Antoniou
Keyword(s):  
Modal Logic ◽  
Semantic Web ◽  
Deontic Logic ◽  
Expressive Power ◽  
Modal Logics ◽  
Cognitive State ◽  
Privacy Requirements ◽  
Defeasible Logic ◽  
Conflicting Information ◽  
Web Information

Defeasible logic is a non-monotonic formalism that deals with incomplete and conflicting information, whereas modal logic deals with the concepts of necessity and possibility. These types of logics play a significant role in the emerging Semantic Web, which enriches the available Web information with meaning, leading to better cooperation between end-users and applications. Defeasible and modal logics, in general, and, particularly, deontic logic provide means for modeling agent communities, where each agent is characterized by its cognitive profile and normative system, as well as policies, which define privacy requirements, access permissions, and individual rights. Toward this direction, this article discusses the extension of DR-DEVICE, a Semantic Web-aware defeasible reasoner, with a mechanism for expressing modal logic operators, while testing the implementation via deontic logic operators, concerned with obligations, permissions, and related concepts. The motivation behind this work is to develop a practical defeasible reasoner for the Semantic Web that takes advantage of the expressive power offered by modal logics, accompanied by the flexibility to define diverse agent behaviours. A further incentive is to study the various motivational notions of deontic logic and discuss the cognitive state of agents, as well as the interactions among them.

scholarly journals Admissible Inference Rules and Semantic Property of Modal Logics

2021 ◽  
Vol 37 ◽  
pp. 104-117
Author(s):  
V.V. Rimatskiy ◽  
Keyword(s):  
Modal Logic ◽  
Inference Rule ◽  
Expressive Power ◽  
Modal Logics ◽  
Human Reasoning ◽  
Inference Rules ◽  
Semantic Property ◽  
Admissible Rule ◽  
Admissible Inference Rules ◽  
Deductive Power

Firstly semantic property of nonstandart logics were described by formulas which are peculiar to studied a models in general, and do not take to consideration a variable conditions and a changing assumptions. Evidently the notion of inference rule generalizes the notion of formulas and brings us more flexibility and more expressive power to model human reasoning and computing. In 2000-2010 a few results on describing of explicit bases for admissible inference rules for nonstandard logics (S4, K4, H etc.) appeared. The key property of these logics was weak co-cover property. Beside the improvement of deductive power in logic, an admissible rule are able to describe some semantic property of given logic. We describe a semantic property of modal logics in term of admissibility of given set of inference rules. We prove that modal logic over logic 𝐺𝐿 enjoys weak co-cover property iff all given rules are admissible for logic.

Modal logics with Belnapian truth values

2010 ◽  
Vol 20 (3) ◽  
pp. 279-304 ◽  
Author(s):  
Serge P Odintsov ◽  
Heinrich Wansing
Keyword(s):  
Modal Logics ◽  
Truth Values

Recursive generation in language

2017 ◽  
Author(s):  
David J. Lobina
Keyword(s):  
Mathematical Logic ◽  
Production System ◽  
General Property ◽  
Recent Literature ◽  
Expressive Power ◽  
The Self ◽  
Recursive Structure ◽  
Embedded Structures ◽  
Mechanical Procedure ◽  
The 1950S

The introduction of recursion into linguistics was the result of applying some of the results of mathematical logic to the study of language. In particular, recursion was introduced in the 1950s as a general property of the mechanical procedure underlying the grammar, in order to account for language’s discrete infinity and expressive power—in the 1950s, this mechanical procedure was a production system, whereas more recently, of course, it is the set-operator merge. Unfortunately, the recent literature has confused the general recursive property of a grammar with specific instances of (recursive) rules/operations within a grammar; more worryingly still, there has been a general conflation of these recursive rules with some of the self-embedded structures these rules can generate, adding to the confusion. The conflation is manifold but always fallacious. Moreover, language manifests a much more generally recursive structure than is usually recognized: bundles of the universal (Specifier)-Head-Complement(s) geometry.

scholarly journals Probability logic: A model-theoretic perspective

2020 ◽  
Author(s):  
M Pourmahdian ◽  
R Zoghifard
Keyword(s):  
Characterization Theorem ◽  
Expressive Power ◽  
Probability Logic ◽  
Theoretic Analysis ◽  
Compactness Property ◽  
Probability Models ◽  
Finitely Additive Probability ◽  
Additive Probability ◽  
Basic Probability ◽  
Abstract Logics

Abstract This paper provides some model-theoretic analysis for probability (modal) logic ($PL$). It is known that this logic does not enjoy the compactness property. However, by passing into the sublogic of $PL$, namely basic probability logic ($BPL$), it is shown that this logic satisfies the compactness property. Furthermore, by drawing some special attention to some essential model-theoretic properties of $PL$, a version of Lindström characterization theorem is investigated. In fact, it is verified that probability logic has the maximal expressive power among those abstract logics extending $PL$ and satisfying both the filtration and disjoint unions properties. Finally, by alternating the semantics to the finitely additive probability models ($\mathcal{F}\mathcal{P}\mathcal{M}$) and introducing positive sublogic of $PL$ including $BPL$, it is proved that this sublogic possesses the compactness property with respect to $\mathcal{F}\mathcal{P}\mathcal{M}$.

The Complexity of Model-Checking Tail-Recursive Higher-Order Fixpoint Logic

2021 ◽  
Vol 178 (1-2) ◽  
pp. 1-30
Author(s):  
Florian Bruse ◽  
Martin Lange ◽  
Etienne Lozes
Keyword(s):  
Model Checking ◽  
Lower Bounds ◽  
Expressive Power ◽  
Higher Order ◽  
Order Logic ◽  
High Complexity ◽  
Transition Systems ◽  
Recursive Formulas ◽  
Second Order Logic ◽  
Monadic Second Order Logic

Higher-Order Fixpoint Logic (HFL) is a modal specification language whose expressive power reaches far beyond that of Monadic Second-Order Logic, achieved through an incorporation of a typed λ-calculus into the modal μ-calculus. Its model checking problem on finite transition systems is decidable, albeit of high complexity, namely k-EXPTIME-complete for formulas that use functions of type order at most k < 0. In this paper we present a fragment with a presumably easier model checking problem. We show that so-called tail-recursive formulas of type order k can be model checked in (k − 1)-EXPSPACE, and also give matching lower bounds. This yields generic results for the complexity of bisimulation-invariant non-regular properties, as these can typically be defined in HFL.

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