Pilar Dellunde

Reputation-based decisions for logic-based cognitive agents

Computational trust and reputation models have been recognized as one of the key technologies required to design and implement agent systems. These models manage and aggregate the information needed by agents to efficiently perform partner selection in uncertain situations. For simple applications, a game theoretical approach similar to that used in most models can suffice. However, if we want to undertake problems found in socially complex virtual societies, we need more sophisticated trust and reputation systems. In this context, reputation-based decisions that agents make take on special relevance and can be as important as the reputation model itself. In this paper, we propose a possible integration of a cognitive reputation model, Repage, into a cognitive BDI agent. First, we specify a belief logic capable to capture the semantics of Repage information, which encodes probabilities. This logic is defined by means of a two first-order languages hierarchy, allowing the specification of axioms as first-order theories. The belief logic integrates the information coming from Repage in terms if image and reputation, and combines them, defining a typology of agents depending of such combination. We use this logic to build a complete graded BDI model specified as a multi-context system where beliefs, desires, intentions and plans interact among each other to perform a BDI reasoning. We conclude the paper with an example and a related work section that compares our approach with current state-of-the-art models.

Some Characterization Theorems for Infinitary Universal Horn Logic Without Equality

In this paper we mainly study preservation theorems for two fragments of the infinitary languages L κ κ , with κ regular, without the equality symbol: the universal Horn fragment and the universal strict Horn fragment. In particular, when κ is ω , we obtain the corresponding theorems for the first-order case. The universal Horn fragment of first-order logic (with equality) has been extensively studied; for references see [10], [7] and [8]. But the universal Horn fragment without equality, used frequently in logic programming, has received much less attention from the model theoretic point of view. At least to our knowledge, the problem of obtaining preservation results for it has not been studied before by model theorists. In spite of this, in the field of abstract algebraic logic we find a theorem which, properly translated, is a preservation result for the strict universal Horn fragment of infinitary languages without equality which, apart from function symbols, have only a unary relation symbol. This theorem is due to J. Czelakowski; see [5], Theorem 6.1, and [6], Theorem 5.1. A. Torrens [12] also has an unpublished result dealing with matrices of sequent calculi which, properly translated, is a preservation result for the strict universal Horn fragment of a first-order language. And in [2] of W. J. Blok and D. Pigozzi we find Corollary 6.3 which properly translated corresponds to our Corollary 19, but for the case of a first-order language that apart from its function symbols has only one κ -ary relation symbol, and for strict universal Horn sentences. The study of these results is the basis for the present work. In the last part of the paper, Section 4, we will make these connections clear and obtain some of these results from our theorems. In this way we hope to make clear two things: (1) The field of abstract algebraic logic can be seen, in part, as a disguised study of universal Horn logic without equality and so has an added interest. (2) A general study of universal Horn logic without equality from a model theoretic point of view can be of help in the field of abstract algebraic logic.

On Elementary Equivalence for Equality-free Logic

This paper is a contribution to the study of equality-free logic, that is, first-order logic without equality. We mainly devote ourselves to the study of algebraic characterizations of its relation of elementary equivalence by provid- ing some Keisler-Shelah type ultrapower theorems and an Ehrenfeucht-Fra¨´ type theorem. We also give characterizations of elementary classes in equality- free logic. As a by-product we characterize the sentences that are logically equivalent to an equality-free one. 1I ntroduction In first-order logic it is common to employ one symbol for the equality relation. Equality is considered a logical notion, with a fixed meaning. This was not the case when the first investigations in mathematical logic took place, but this practice has been strongly supported by successful applications to mathematical theories. Thus, the general study of first-order logic without equality, or equality-free logic ,a sw eprefer to call it, has been neglected in favor of the more powerful version with equality. Recently some interest in fragments of equality-free logic has arisen in the frame of algebraic logic (see Blok and Pigozzi (5) and Bloom (2)). We think that a model-theoretic study of equality-free logic is worthwhile by itself and we hope that, by means of contrast with the well-known results for first-order logic, this study will contribute to the understanding of the role of equality in mathematical theories and structures. As an easy example of this comparison consider the fact that every satisfiable set of equality-free sentences has an infinite model. Let L be a similarity type. The set of equality-free formulas of L, that is, the set of all first-order formulas of L not containing the equality symbol, is denoted by L − . Given two L-structures A, B with A ≡ − B we mean that A and B satisfy exactly the same sentences of L − .W edevote this paper to the study of algebraic characteri- zations of the relation ≡ − and of elementary classes in the sense of L − .

Deductive Coherence and Norm Adoption

This paper is a contribution to the formalisation of Thagard’s coherence theory. The term coherence is defined as the quality or the state of cohering, especially a logical, orderly, and aesthetically consistent relationship of parts. A coherent set is interdependent such that every element in it contributes to the coherence. We take Thagard’s proposal of a coherence set as that of maximising satisfaction of constraints between elements and explore its use in normative multiagent systems. In particular, we interpret coherence maximisation as a decision-making criterion for norm adoption. We first provide a general coherence framework with the necessary computing tools. Later we introduce a proof-theoretic characterisation of a particular type of coherence, namely the deductive coherence based on Thagard’s principles, and derive a mechanism to compute coherence values between elements in a deductive coherence graph. Our use of graded logic helps us to incorporate reasoning under uncertainty, which is more realistic in the context of multiagent systems. We then conduct a case study where agents deliberate about norm adoption in a multiagent system where there is competition for a common resource. We show how a coherence-maximising agent decides to violate a norm guided by its coherence.

Equality-free logic: the method of diagrams and preservation theorems

In this article I prove preservation theorems for the positive and for the universal-existential fragment of equality-free logic. I give a systematic presentation of the method of diagrams for rst-order languages without equality.

Introducing Grades in Deontic Logics

In this paper we define a framework to introduce gradedness in Deontic logics through the use of fuzzy modalities. By way of example, we instantiate the framework to Standard Deontic logic (SDL) formulas. Given a deontic formula ?? SDL, our language contains formulas of the form

Preserving mappings in fuzzy predicate logics

\overline{r} \to N\Phi

Extending possibilistic logic over Gödel logic

or

A defeasible reasoning model of inductive concept learning from examples and communication

\overline{r} \to P\Phi

Löwenheim–Skolem theorems for non-classical first-order algebraizable logics

, where r? [0, 1], expressing that the preference or probability degree respectively of a norm ?is at least r. We present sound and complete axiomatisations for these logics.