World Semantics Research Articles

Natural Deduction for Modal Logic with a Backtracking Operator

Harold Hodes in [1] introduces an extension of first-order modal logic featuring a backtracking operator, and provides a possible worlds semantics, according to which the operator is a kind of device for ‘world travel’; he does not provide a proof theory. In this paper, I provide a natural deduction system for modal logic featuring this operator, and argue that the system can be motivated in terms of a reading of the backtracking operator whereby it serves to indicate modal scope. I prove soundness and completeness theorems with respect to Hodes’ semantics, as well as semantics with fewer restrictions on the accessibility relation (Hodes restricts his attentionto S5).

GML-Based Data Management and Semantic World Modelling for a 4D Forest Simulation and Information System

Various types of 3D simulation applications benefit from realistic forest models. They range from flight simulators for entertainment to harvester simulators for training and tree growth simulations for research and planning. This paper's 4D forest simulation and information system integrates the necessary methods for data extraction, modelling and management. Using modern methods of semantic world modelling, tree data can efficiently be extracted from remote sensing data. The derived forest models contain position, height, crown volume, type and diameter of each tree. This data is modelled using GML-based data models to assure compatibility and exchangeability. ForestGML is the name of a new schema family developed to provide a common basis for forestry data. A flexible approach for database synchronization is used to manage the data and provide caching, persistence, a central communication hub for change distribution, and a versioning mechanism. Combining various simulation techniques and data versioning, the 4D forest simulation and information system can provide applications with “both directions” of the fourth dimension. This paper outlines the current state, new developments, and integration of tree extraction, data modelling, and data management. It also shows several applications realized with the system.

Modalities for an Allegorical Conceptual Data Model

Allegories are enriched categories generalizing a category of sets and binary relations. In this paper, we extend a new, recently-introduced conceptual data model based on allegories by adding support for modal operators and developing a modal interpretation of the model in any allegory satisfying certain additional (but natural) axioms. The possibility of using different allegories allows us to transparently use alternative logical frameworks, such as fuzzy relations. Mathematically, our work demonstrates how to enrich with modal operators and to give a many world semantics to an abstract algebraic logic framework. We also give some examples of applications of the modal extension.

Mining Probabilistically Frequent Sequential Patterns in Large Uncertain Databases

Data uncertainty is inherent in many real-world applications such as environmental surveillance and mobile tracking. Mining sequential patterns from inaccurate data, such as those data arising from sensor readings and GPS trajectories, is important for discovering hidden knowledge in such applications. In this paper, we propose to measure pattern frequentness based on the possible world semantics. We establish two uncertain sequence data models abstracted from many real-life applications involving uncertain sequence data, and formulate the problem of mining probabilistically frequent sequential patterns (or p-FSPs) from data that conform to our models. However, the number of possible worlds is extremely large, which makes the mining prohibitively expensive. Inspired by the famous PrefixSpan algorithm, we develop two new algorithms, collectively called U-PrefixSpan, for p-FSP mining. U-PrefixSpan effectively avoids the problem of “possible worlds explosion”, and when combined with our four pruning and validating methods, achieves even better performance. We also propose a fast validating method to further speed up our U-PrefixSpan algorithm. The efficiency and effectiveness of U-PrefixSpan are verified through extensive experiments on both real and synthetic datasets.

Lowe's Argument Against the Psychoneural Token Identity Thesis

AbstractE. J. Lowe argues that the mental event token cannot be identical to the complex neural event token for they have different counterfactual properties. If the mental event had not occurred, the behavior would not have ensued, while if the neural event had not occurred, the behavior would have ensued albeit slightly differently. Lowe's argument for the neural counterfactual relies on standard possible world semantics, whose evaluation of such counterfactuals is problematic. His argument for the mental counterfactual relies on a premise that is plausibly false. My arguments support other counterfactuals, which are consistent with identity theories.

Quasi-SLCA Based Keyword Query Processing over Probabilistic XML Data

The probabilistic threshold query is one of the most common queries in uncertain databases, where a result satisfying the query must be also with probability meeting the threshold requirement. In this paper, we investigate probabilistic threshold keyword queries (PrTKQ) over XML data, which is not studied before. We first introduce the notion of quasi-SLCA and use it to represent results for a PrTKQ with the consideration of possible world semantics. Then we design a probabilistic inverted (PI) index that can be used to quickly return the qualified answers and filter out the unqualified ones based on our proposed lower/upper bounds. After that, we propose two efficient and comparable algorithms: Baseline Algorithm and PI index-based Algorithm. To accelerate the performance of algorithms, we also utilize probability density function. An empirical study using real and synthetic data sets has verified the effectiveness and the efficiency of our approaches.

Humean Supervenience and Multidimensional Semantics

What distinguishes indicative conditionals from subjunctive conditionals, according to one popular view, is that the so-called Adams’ thesis holds for the former kind of conditionals but the so-called Skyrms’ thesis for the latter. According to a plausible metaphysical view, both conditionals and chances supervene on non-modal facts. But since chances do not supervene on facts about particular events but facts about event-types, the past as well as the future is chancy. Some philosophers have worried that this metaphysical view is incompatible with the aforementioned view on the probability of conditionals. This paper however shows that there is no need to worry, as these views can all be simultaneously satisfied within the so-called Multidimensional Possible World Semantics for conditionals.

Pragmatism, Idealism, and the Modal Menace: Rorty, Brandom, and Truths about Photons

In a short exchange published in 2000, Richard Rorty and Robert Brandom differed over the status of “facts” in a world containing no speakers and, hence, no speech acts. While Brandom wanted to retain the meaningfulness of talk of “facts” or “truths” about things—in this case truths about photons—in a world in which there could be no claimings about such things, Rorty denied the existence of any such “worldly items” as “facts.” In this essay the difference between Rorty and Brandom on this issue is used to explore their differing attitudes to modality. Brandom appeals to a Kantian approach of modal realism to support counterfactual claims. However, I argue that when his approach to modality is examined in the context of current debates over possible world semantics, his own “incompatibilist” semantics itself seems incompatible with a Kantian approach to modality. In turn, I suggest that this difference between Brandom and Rorty in their attitudes to modality reveals a difference in their respective attitudes to pragmatism’s relation to philosophy in general.

Ontological Argument: Two-Dimensional Version

The ontological argument has been reintroduced into the area of analytical metaphysics in 20th century due to the development of modal logic and possible worlds semantics. However, there are few attempts to approach this argument with two-dimensional possible worlds framework. The present paper provides a new two-dimensional interpretation of Anselm's proof in terms of modal logic with an actuality operator (AML). It is argued that the standard modal explications of Anselm’s enigmatic concept "greater" and its connection with the concept of "actuality" have some essential shortcomings compared with the two-dimensional approach.

A Lewisian Trilemma

AbstractAccording to one reading of the thesis of Humean Supervenience, most famously defended by David Lewis, certain ‘fundamental’ (non‐modal) facts entail all there is but do not supervene on less fundamental facts. However, in this paper I prove that it follows from Lewis' possible world semantics for counterfactuals, in particular his Centring condition, that all non‐modal facts supervene on counterfactuals. Humeans could respond to this result by either giving up Centring or abandoning the idea that the most fundamental facts do not supervene on less fundamental facts. I argue that either response should in general be acceptable to Humeans: the first since there is nothing particularly Humean about Centring; the latter since Humeans should, independently of the result I present, be sceptical that the supervenience of one fact upon another by itself says anything about ‘fundamentality’.

Montague’s Theorem and Modal Logic

In the present piece we defend predicate approaches to modality, that is approaches that conceive of modal notions as predicates applicable to names of sentences or propositions, against the challenges raised by Montague’s theorem. Montague’s theorem is often taken to show that the most intuitive modal principles lead to paradox if we conceive of the modal notion as a predicate. Following Schweizer (J Philos Logic 21:1–31, 1992) and others we show this interpretation of Montague’s theorem to be unwarranted unless a further non trivial assumption is made—an assumption which should not be taken as a given. We then move on to showing, elaborating on work of Gupta (J Philos Logic 11:1–60, 1982), Asher and Kamp (Properties, types, and meaning. Vol. I: foundational issues, Kluwer, Dordrecht, pp 85−158, 1989), and Schweizer (J Philos Logic 21:1–31, 1992), that the unrestricted modal principles can be upheld within the predicate approach and that the predicate approach is an adequate approach to modality from the perspective of modal operator logic. To this end we develop a possible world semantics for multiple modal predicates and show that for a wide class of multimodal operator logics we may find a suitable class of models of the predicate approach which satisfies, modulo translation, precisely the theorems of the modal operator logic at stake.

SEMANTIC WORLD MODELLING AND DATA MANAGEMENT IN A 4D FOREST SIMULATION AND INFORMATION SYSTEM

Abstract. Various types of 3D simulation applications benefit from realistic forest models. They range from flight simulators for entertainment to harvester simulators for training and tree growth simulations for research and planning. Our 4D forest simulation and information system integrates the necessary methods for data extraction, modelling and management. Using modern methods of semantic world modelling, tree data can efficiently be extracted from remote sensing data. The derived forest models contain position, height, crown volume, type and diameter of each tree. This data is modelled using GML-based data models to assure compatibility and exchangeability. A flexible approach for database synchronization is used to manage the data and provide caching, persistence, a central communication hub for change distribution, and a versioning mechanism. Combining various simulation techniques and data versioning, the 4D forest simulation and information system can provide applications with "both directions" of the fourth dimension. Our paper outlines the current state, new developments, and integration of tree extraction, data modelling, and data management. It also shows several applications realized with the system.

Possible world semantics for first-order logic of proofs

In the tech report Artemov and Yavorskaya (Sidon) (2011) [4] an elegant formulation of the first-order logic of proofs was given, FOLP. This logic plays a fundamental role in providing an arithmetic semantics for first-order intuitionistic logic, as was shown. In particular, the tech report proved an arithmetic completeness theorem, and a realization theorem for FOLP. In this paper we provide a possible-world semantics for FOLP, based on the propositional semantics of Fitting (2005) [5]. We also give an Mkrtychev semantics. Motivation and intuition for FOLP can be found in Artemov and Yavorskaya (Sidon) (2011) [4], and are not fully discussed here.This paper is dedicated to Sergei Artemov, an honored colleague and friend, who has made wonderful things for the rest of us to play with.

An Improved Algorithm for Efficient Mining of Frequent Item Sets on Large Uncertain Databases

The data handled in emerging applications like location based services, sensor monitoring systems, and data integration, are often inexact in nature. In this paper, the important problem of extracting frequent item sets from a large uncertain database, interpreted under the Possible World Semantics (PWS) is presented. This issue is technically challenging, since an uncertain database contains an exponential number of possible worlds. By observing that the mining process can be modeled as a Poisson binomial distribution, an algorithm was developed, which can efficiently and accurately discover frequent item sets in a large uncertain database. The important issue of maintaining the mining result for a database that is evolving (e.g., by inserting a tuple) can be presented. Specifically, the proposed mining algorithm can enable Probabilistic Frequent Item set (PFI) results to be refreshed. This reduces the need of re-executing the whole mining algorithm on the new database, which is often more expensive and unnecessary. The proposed algorithm can support incremental mining and provides the accurate results on mining the uncertain database. The extensive evaluation on real data set to validate the approach is performed.

Description logics of context

We introduce Description Logics of Context (DLCs)—an extension of Description Logics (DLs) for context-based reasoning. Our approach descends from J. McCarthy's tradition of treating contexts as formal objects over which one can quantify and express first-order properties. DLCs are founded in two-dimensional possible world semantics, where one dimension represents a usual object domain and the other a domain of contexts, and accommodate two interacting DL languages—the object and the context language—interpreted over their respective domains. Effectively, DLCs comprise a family of two-sorted , two-dimensional combinations of pairs of DLs. We argue that this setup ensures a well-grounded, generic framework for capturing and studying mechanisms of contextualization in the DL paradigm. As the main technical contribution, we prove 2ExpTime-completeness of the satisfiability problem in the maximally expressive DLC, based on the DL forumla . As an interesting corollary, we show that under certain conditions this result holds also for a range of two-dimensional DLs, including the prominent forumla .

Tree Species Classification and Input Data Evaluation

Semantic world models require detailed classifications that allow the generation of entities that represent real world objects. This study combines advanced binary support vector machine classifiers in the hierarchical structure of a binary decision tree. This approach fulfills the requirements of a subsequent semantic model generation approach as it is an object based approach that works on the single tree level. It is fast and can be applied easily without expert knowledge. The algorithm can be trained on existing tree sample inventory data and additional samples from other data sources can be imported or placed. Classification results were calculated on a variety of input data sources and spatial resolutions. The achieved accuracies were analyzed and provide information for the decision support regarding input data choice for future applications.

Efficient Mining of Frequent Item Sets on Large Uncertain Databases

The data handled in emerging applications like location-based services, sensor monitoring systems, and data integration, are often inexact in nature. In this paper, we study the important problem of extracting frequent item sets from a large uncertain database, interpreted under the Possible World Semantics (PWS). This issue is technically challenging, since an uncertain database contains an exponential number of possible worlds. By observing that the mining process can be modeled as a Poisson binomial distribution, we develop an approximate algorithm, which can efficiently and accurately discover frequent item sets in a large uncertain database. We also study the important issue of maintaining the mining result for a database that is evolving (e.g., by inserting a tuple). Specifically, we propose incremental mining algorithms, which enable Probabilistic Frequent Item set (PFI) results to be refreshed. This reduces the need of re-executing the whole mining algorithm on the new database, which is often more expensive and unnecessary. We examine how an existing algorithm that extracts exact item sets, as well as our approximate algorithm, can support incremental mining. All our approaches support both tuple and attribute uncertainty, which are two common uncertain database models. We also perform extensive evaluation on real and synthetic data sets to validate our approaches.

Behavioral architecture of the cortical sheet

Summary The effortless ability of vertebrates to explore and exploit their environment is strongly correlated with the evolution of the most anterior part of their nervous system, the forebrain, where data from autonomic (visceral), limbic (emotive), and internal and peripheral sensors of the external world are combined to develop, decide, and deploy advantageous behaviors. The correlation of behavioral performance with forebrain expansion suggests that evolution has discovered the developmental means of building vertebrate brains to produce a scalable, special-purpose architecture for efficiently processing and expressing behavior. In mammals, the exuberant expansion of this forebrain is dominated by the growth of their cortex — the two-dimensional sheet that is the major source of their intelligent behavior, especially for primates.

Domain Ontology, an Instrument of Semantic Web Knowledge Management in e-Learning

Domain ontology is proposed as an instrument for controlling of e-learning course results. This approach instead of traditional testing more objectively reflects the structure of studentsâ?? knowledge. Use of ontologies for knowledge representation provides interoperability of the used testing systems. The domain knowledge has been found and reuse in the semantic web world. Domain ontology developing is based on the principles of ontological analysis. The method of itâ??s use for evaluation of the learnersâ?? knowledge results is based on matching of the learnersâ?? ontology with the reference ontology proposed by the trainer/tutor. A multi-agent system for e-learning (M(e)L ) has been defined and a prototype system has been developed. In a case, the domain ontology and the semantic web representation has been applied in two e-learning university courses.

Model-based probabilistic frequent itemset mining

Data uncertainty is inherent in emerging applications such as location-based services, sensor monitoring systems, and data integration. To handle a large amount of impre- cise information, uncertain databases have been recently developed. In this paper, we study how to efficiently discover frequent itemsets from large uncertain databases, interpreted under the Possible World Semantics. This is technically challenging, since an uncertain data- base induces an exponential number of possible worlds. To tackle this problem, we propose a novel methods to capture the itemset mining process as a probability distribution func- tion taking two models into account: the Poisson distribution and the normal distribution. These model-based approaches extract frequent itemsets with a high degree of accuracy and