Distinguished algebraic semantics for t-norm based fuzzy logics:Methods and algebraic equivalencies

This paper is a contribution to Mathematical fuzzy logic, in particular to the algebraic study of t-norm based fuzzy logics. In the general framework of propositional core and ?-core fuzzy logics we consider three properties of completeness with respect to any semantics of linearly ordered algebras. Useful algebraic characterizations of these completeness properties are obtained and their relations are studied. Moreover, we concentrate on five kinds of distinguished semantics for these logics-namely the class of algebras defined over the real unit interval, the rational unit interval, the hyperreals (all ultrapowers of the real unit interval), the strict hyperreals (only ultrapowers giving a proper extension of the real unit interval) and finite chains, respectively-and we survey the known completeness methods and results for prominent logics. We also obtain new interesting relations between the real, rational and (strict) hyperreal semantics, and good characterizations for the completeness with respect to the semantics of finite chains. Finally, all completeness properties and distinguished semantics are also considered for the first-order versions of the logics where a number of new results are proved. © 2009 Elsevier B.V. All rights reserved.

Decoding semantics across fMRI sessions with different stimulus modalities:a practical MVPA study

Both embodied and symbolic accounts of conceptual organization would predict partial sharing and partial differentiation between the neural activations seen for concepts activated via different stimulus modalities. But cross-participant and cross-session variability in BOLD activity patterns makes analyses of such patterns with MVPA methods challenging. Here, we examine the effect of cross-modal and individual variation on the machine learning analysis of fMRI data recorded during a word property generation task. We present the same set of living and non-living concepts (land-mammals, or work tools) to a cohort of Japanese participants in two sessions: the first using auditory presentation of spoken words; the second using visual presentation of words written in Japanese characters. Classification accuracies confirmed that these semantic categories could be detected in single trials, with within-session predictive accuracies of 80-90%. However cross-session prediction (learning from auditory-task data to classify data from the written-word-task, or vice versa) suffered from a performance penalty, achieving 65-75% (still individually significant at p « 0.05). We carried out several follow-on analyses to investigate the reason for this shortfall, concluding that distributional differences in neither time nor space alone could account for it. Rather, combined spatio-temporal patterns of activity need to be identified for successful cross-session learning, and this suggests that feature selection strategies could be modified to take advantage of this.

Improving the Semantics of Conceptual-Modeling Grammars:A New Perspective on an Old Problem

A core activity in information systems development involves understanding the
conceptual model of the domain that the information system supports. Any conceptual model is ultimately created using a conceptual-modeling (CM) grammar. Accordingly, just as high quality conceptual models facilitate high quality systems development, high quality CM grammars facilitate high quality conceptual modeling. This paper seeks to provide a new perspective on improving the quality of CM grammar semantics. For the past twenty years, the leading approach to this topic has drawn on ontological theory. However, the ontological approach captures just half of the story. It needs to be coupled with a logical approach. We show how ontological quality and logical quality interrelate and we outline three contributions of a logical approach: the ability to see familiar conceptualmodeling problems in simpler ways, the illumination of new problems, and the ability to prove the benefit of modifying CM grammars.

Can(Plan)+: Extending the Operational Semantics of the BDI Architecture to deal with Uncertain Information

The BDI architecture, where agents are modelled based on their beliefs, desires and intentions, provides a practical approach to develop large scale systems. However, it is not well suited to model complex Supervisory Control And Data Acquisition (SCADA) systems pervaded by uncertainty. In this paper we address this issue by extending the operational semantics of Can(Plan) into Can(Plan)+. We start by modelling the beliefs of an agent as a set of epistemic states where each state, possibly using a different representation, models part of the agent's beliefs. These epistemic states are stratified to make them commensurable and to reason about the uncertain beliefs of the agent. The syntax and semantics of a BDI agent are extended accordingly and we identify fragments with computationally efficient semantics. Finally, we examine how primitive actions are affected by uncertainty and we define an appropriate form of lookahead planning.

Operators for Similarity Search: Semantics, Techniques and Usage Scenarios

This book provides a comprehensive tutorial on similarity operators. The authors systematically survey the set of similarity operators, primarily focusing on their semantics, while also touching upon mechanisms for processing them effectively.

The book starts off by providing introductory material on similarity search systems, highlighting the central role of similarity operators in such systems. This is followed by a systematic categorized overview of the variety of similarity operators that have been proposed in literature over the last two decades, including advanced operators such as RkNN, Reverse k-Ranks, Skyline k-Groups and K-N-Match. Since indexing is a core technology in the practical implementation of similarity operators, various indexing mechanisms are summarized. Finally, current research challenges are outlined, so as to enable interested readers to identify potential directions for future investigations.

In summary, this book offers a comprehensive overview of the field of similarity search operators, allowing readers to understand the area of similarity operators as it stands today, and in addition providing them with the background needed to understand recent novel approaches.

Semantics for possibilistic answer set programs: uncertain rules versus rules with uncertain conclusions

Although Answer Set Programming (ASP) is a powerful framework for declarative problem solving, it cannot in an intuitive way handle situations in which some rules are uncertain, or in which it is more important to satisfy some constraints than others. Possibilistic ASP (PASP) is a natural extension of ASP in which certainty weights are associated with each rule. In this paper we contrast two different views on interpreting the weights attached to rules. Under the first view, weights reflect the certainty with which we can conclude the head of a rule when its body is satisfied. Under the second view, weights reflect the certainty that a given rule restricts the considered epistemic states of an agent in a valid way, i.e. it is the certainty that the rule itself is correct. The first view gives rise to a set of weighted answer sets, whereas the second view gives rise to a weighted set of classical answer sets.

Characterizing and Extending Answer Set Semantics using Possibility Theory

Answer Set Programming (ASP) is a popular framework for modelling combinatorial problems. However, ASP cannot be used easily for reasoning about uncertain information. Possibilistic ASP (PASP) is an extension of ASP that combines possibilistic logic and ASP. In PASP a weight is associated with each rule, whereas this weight is interpreted as the certainty with which the conclusion can be established when the body is known to hold. As such, it allows us to model and reason about uncertain information in an intuitive way. In this paper we present new semantics for PASP in which rules are interpreted as constraints on possibility distributions. Special models of these constraints are then identified as possibilistic answer sets. In addition, since ASP is a special case of PASP in which all the rules are entirely certain, we obtain a new characterization of ASP in terms of constraints on possibility distributions. This allows us to uncover a new form of disjunction, called weak disjunction, that has not been previously considered in the literature. In addition to introducing and motivating the semantics of weak disjunction, we also pinpoint its computational complexity. In particular, while the complexity of most reasoning tasks coincides with standard disjunctive ASP, we find that brave reasoning for programs with weak disjunctions is easier.