The Expressive Power of k-ary Exclusion Logic

In this paper we study the expressive power of k-ary exclusion logic, EXC[k], that is obtained by extending first order logic with k-ary exclusion atoms. It is known that without arity bounds exclusion logic is equivalent with dependence logic. By observing the translations, we see that the expressive power of EXC[k] lies in between k-ary and (k+1)-ary dependence logics. We will show that, at least in the case of k=1, the both of these inclusions are proper. In a recent work by the author it was shown that k-ary inclusion-exclusion logic is equivalent with k-ary existential second order logic, ESO[k]. We will show that, on the level of sentences, it is possible to simulate inclusion atoms with exclusion atoms, and this way express ESO[k]-sentences by using only k-ary exclusion atoms. For this translation we also need to introduce a novel method for "unifying" the values of certain variables in a team. As a consequence, EXC[k] captures ESO[k] on the level of sentences, and we get a strict arity hierarchy for exclusion logic. It also follows that k-ary inclusion logic is strictly weaker than EXC[k]. Finally we will use similar techniques to formulate a translation from ESO[k] to k-ary inclusion logic with strict semantics. Consequently, for any arity fragment of inclusion logic, strict semantics is more expressive than lax semantics.Comment: Preprint of a paper in the special issue of WoLLIC2016 in Annals of Pure and Applied Logic, 170(9):1070-1099, 201

Modeling Adversaries in a Logic for Security Protocol Analysis

Logics for security protocol analysis require the formalization of an adversary model that specifies the capabilities of adversaries. A common model is the Dolev-Yao model, which considers only adversaries that can compose and replay messages, and decipher them with known keys. The Dolev-Yao model is a useful abstraction, but it suffers from some drawbacks: it cannot handle the adversary knowing protocol-specific information, and it cannot handle probabilistic notions, such as the adversary attempting to guess the keys. We show how we can analyze security protocols under different adversary models by using a logic with a notion of algorithmic knowledge. Roughly speaking, adversaries are assumed to use algorithms to compute their knowledge; adversary capabilities are captured by suitable restrictions on the algorithms used. We show how we can model the standard Dolev-Yao adversary in this setting, and how we can capture more general capabilities including protocol-specific knowledge and guesses.Comment: 23 pages. A preliminary version appeared in the proceedings of FaSec'0

Space-contained conflict revision, for geographic information

Using qualitative reasoning with geographic information, contrarily, for instance, with robotics, looks not only fastidious (i.e.: encoding knowledge Propositional Logics PL), but appears to be computational complex, and not tractable at all, most of the time. However, knowledge fusion or revision, is a common operation performed when users merge several different data sets in a unique decision making process, without much support. Introducing logics would be a great improvement, and we propose in this paper, means for deciding -a priori- if one application can benefit from a complete revision, under only the assumption of a conjecture that we name the "containment conjecture", which limits the size of the minimal conflicts to revise. We demonstrate that this conjecture brings us the interesting computational property of performing a not-provable but global, revision, made of many local revisions, at a tractable size. We illustrate this approach on an application.Comment: 14 page

Modal logics are coalgebraic

Applications of modal logics are abundant in computer science, and a large number of structurally different modal logics have been successfully employed in a diverse spectrum of application contexts. Coalgebraic semantics, on the other hand, provides a uniform and encompassing view on the large variety of specific logics used in particular domains. The coalgebraic approach is generic and compositional: tools and techniques simultaneously apply to a large class of application areas and can moreover be combined in a modular way. In particular, this facilitates a pick-and-choose approach to domain specific formalisms, applicable across the entire scope of application areas, leading to generic software tools that are easier to design, to implement, and to maintain. This paper substantiates the authors' firm belief that the systematic exploitation of the coalgebraic nature of modal logic will not only have impact on the field of modal logic itself but also lead to significant progress in a number of areas within computer science, such as knowledge representation and concurrency/mobility