Towards KEM Unification

This paper highlights a particular construction of a correct KEM without failures and without ciphertext expansion from any correct deterministic PKE, and presents a simple tight proof of ROM IND-CCA2 security for the KEM assuming merely OW-CPA security for the PKE. Compared to previous proofs, this proof is simpler, and is also factored into smaller pieces that can be audited independently. In particular, this paper introduces the notion of ``IND-Hash\u27\u27 security and shows that this allows a new separation between checking encryptions and randomizing decapsulations. The KEM is easy to implement in constant time, given a constant-time implementation of the PKE

Modal tableaux for nonmonotonic reasoning

The tableau-like proof system KEM has been proven to be able to cope with a wide variety of (normal) modal logics. KEM is based on D'Agostino and Mondadori's (1994) classical proof system KE, a combination of tableau and natural deduction inference rules which allows for a restricted ("analytic") Use of the cut rule. The key feature of KEM, besides its being based neither on resolution nor on standard sequent/tableau inference techniques, is that it generates models and checks them using a label scheme to bookkeep "world" paths. This formalism can be extended to handle various system of multimodal logic devised for dealing with nonmonotonic reasoning, by relying in particular on Meyer and van der Hoek's (1992) logic for actuality and preference. In this paper we shall be concerned with developing a similar extension this time by relying on Schwind and Siegel's (1993,1994) system H, another multimodal logic devised for dealing with nonmonotonic inference

Labelled Modal Tableaux

Labelled tableaux are extensions of semantic tableaux with annotations (labels, indices) whose main function is to enrich the modal object language with semantic elements. This paper consists of three parts. In the first part we consider some options for labels: simple constant labels vs labels with free variables, logic depended inference rules vs labels manipulation based on a label algebra. In the second and third part we concentrate on a particular labelled tableaux system called KEM using free variable and a specialised label algebra. Specifically in the second part we show how labelled tableaux (KEM) can account for different types of logics (e.g., non-normal modal logics and conditional logics). In the third and final part we investigate the relative complexity of labelled tableaux systems and we show that the uses of KEM's label algebra can lead to speed up on proofs

Ideality and subideality from a computational point of view

Why should Law need automated proof systems? The answer to this question implies an answer to the following question: Is logic needed in Law? In fact it has been argued that logics are useless for Law (see, for example, Kelsen 1989). We believe that logic, and deontic logics in particular - but also modal logics - have a role to play in Law; for example if one wants to study what the relationships are among the various degrees of adjudication in Italian Law, one should note that they give rise to a transitive, irreflexive and finite structure, which is the frame of the modal logic of provability GL; one of the most important properties of such a logic is that no system, (no court) in this frame, could claim its own correctness without becoming incorrect (Boolos 1993, Smullyan 1988), but the correctness of a lower court can be established by a higher one. This example shows that the study of modal logic can help in finding certain already known properties of legal systems. Moreover, each time we are dealing with the notions of Obligation and Permission, and we are interested in the study of their mutual relationship, we can arrange them into a deontic framework, thus producing a certain kind of deontic logic. Finally a hint for the use of logic in legal reasoning is given, for example in the Italian case, by the law itself; in fact article 192, 1 comma of the "Italian code of criminal procedure" prescribes that the judges state the reasons of their adjudication; moreover several other articles of the same code, state: when evidence is valid, how evidence should be used in order to lead to an adjudication, etc. On this basis the "Italian code of criminal procedure" can be thought of as a deductive system where its articles act as the inference rules, whereas the articles of the "Italian code of criminal law" are the axioms. What does a proof system do? A proof system can work in two ways. The first of them consists of producing admissible steps one after the other according to the inference rules; in this way each step is guaranteed to be correct, but we are not led to the goal we want to prove. The other one consists of verifying whether a conclusion follows from given premises, i.e., if the adjudication follows logically from the evidence, mainly by refuting the negation of the conclusion. The system we propose is based on the logic of ideality and subideality developed by Jones and Porn, and it verifies in the above mentioned logical framework whether a given conclusion follows from given premises. Moreover, due to its basic control structure it can also be used as an analytic direct proof system

Labelling Ideality and Subideality

In this paper we suggest ways in which logic and law may usefully relate; and we present an analytic proof system dealing with the Jones Porn's deontic logic of Ideality and Subideality, which offers some suggestions about how to embed legal systems in label formalism

Labelled tableaux for nonmonotonic reasoning: Cumulative consequence relations

In this paper we present a labelled proof method for computing nonmonotonic consequence relations in a conditional logic setting. The method exploits the strong connection between these deductive relations and conditional logics, and it is based on the usual possible world semantics devised for the latter. The label formalism KEM, introduced to account for the semantics of normal modal logics, is easily adapted to the semantics of conditional logic by simply indexing labels with formulas. The basic inference rules are provided by the propositional system KE+ - a tableau-like analytic proof system devised to be used both as a refutation method and a direct method of proof - that is the classical core of KEM which is thus enlarged with suitable elimination rules for the conditional connective. The resulting algorithmic framework is able to compute cumulative consequence relations in so far as they can be expressed as conditional implications

Gravitational Phenomena from Superstrings in Curved Spacetime

The four-dimensional superstring solutions define at low energy effective supergravity theories. A class of them extends successfully the validity of the standard model up to the string scale (${\cal O}(10^{17})~TeV$). We stress the importance of string corrections which are relevant for low energy (${\cal O}(1)~TeV$) predictions of gauge and Yukawa couplings as well as the spectrum of the supersymmetric particles. A class of exact string solutions are also presented, providing non trivial space-time backgrounds, from which we can draw some lessons concerning the regions of space-time where the notion of the effective field theory prescription make sense. We show that the string gravitational phenomena may induce during the cosmological evolution, transitions from one effective field theory prescription to a different one where the geometrical and topological data, as well as the relevant observable states are drastically different. Talk presented by C. Kounnas in the XXIX Moriond Meeting, M\'eribel, France.Comment: LateX, 11pp., CERN-TH.7332/9

Modal tableaux for verifying stream authentication protocols

To develop theories to specify and reason about various aspects of multi-agent systems, many researchers have proposed the use of modal logics such as belief logics, logics of knowledge, and logics of norms. As multi-agent systems operate in dynamic environments, there is also a need to model the evolution of multi-agent systems through time. In order to introduce a temporal dimension to a belief logic, we combine it with a linear-time temporal logic using a powerful technique called fibring for combining logics. We describe a labelled modal tableaux system for the resulting fibred belief logic (FL) which can be used to automatically verify correctness of inter-agent stream authentication protocols. With the resulting fibred belief logic and its associated modal tableaux, one is able to build theories of trust for the description of, and reasoning about, multi-agent systems operating in dynamic environments