arXiv subjects

Riccardo Pucella

Publications and source records attributed to Riccardo Pucella.

At least 19 recordsLinked to original sources

arXiv2017

An Epistemic Foundation for Authentication Logics (Extended Abstract)

While there have been many attempts, going back to BAN logic, to base reasoning about security protocols on epistemic notions, they have not been all that successful. Arguably, this has been due to the particular logics chosen. We present a simple logic based on the well-understood modal operators of knowledge, time, and probability, and show that it is able to handle issues that have often been swept under the rug by other approaches, while being flexible enough to capture all the higher- level security notions that appear in BAN logic. Moreover, while still assuming that the knowledge operator allows for unbounded computation, it can handle the fact that a computationally bounded agent cannot decrypt messages in a natural way, by distinguishing strings and message terms. We demonstrate that our logic can capture BAN logic notions by providing a translation of the BAN operators into our logic, capturing belief by a form of probabilistic knowledge.

cs.CR↗

arXiv2014

A Logic for Reasoning about Upper Probabilities

We present a propositional logic to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and complete axiomatization for the logic, and show that the satisfiability problem is NP-complete, no harder than satisfiability for propositional logic.

cs.AI↗

arXiv2014

Reasoning about Expectation

Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the underlying representation of uncertainty. We give sound and complete axiomatizations for the logic in the case that the underlying representation is (a) probability, (b) sets of probability measures, (c) belief functions, and (d) possibility measures. We show that this logic is more expressive than the corresponding logic for reasoning about likelihood in the case of sets of probability measures, but equi-expressive in the case of probability, belief, and possibility. Finally, we show that satisfiability for these logics is NP-complete, no harder than satisfiability for propositional logic.

cs.AI↗

arXiv2014

A Logic for Reasoning about Evidence

We introduce a logic for reasoning about evidence, that essentially views evidence as a function from prior beliefs (before making an observation) to posterior beliefs (after making the observation). We provide a sound and complete axiomatization for the logic, and consider the complexity of the decision problem. Although the reasoning in the logic is mainly propositional, we allow variables representing numbers and quantification over them. This expressive power seems necessary to capture important properties of evidence

cs.AI↗

arXiv2014

Evidence with Uncertain Likelihoods

An agent often has a number of hypotheses, and must choose among them based on observations, or outcomes of experiments. Each of these observations can be viewed as providing evidence for or against various hypotheses. All the attempts to formalize this intuition up to now have assumed that associated with each hypothesis h there is a likelihood function μh, which is a probability measure that intuitively describes how likely each observation is, conditional on h being the correct hypothesis. We consider an extension of this framework where there is uncertainty as to which of a number of likelihood functions is appropriate, and discuss how one formal approach to defining evidence, which views evidence as a function from priors to posteriors, can be generalized to accommodate this uncertainty.

cs.AI↗

arXiv2013

Knowledge and Security

Epistemic concepts, and in some cases epistemic logic, have been used in security research to formalize security properties of systems. This survey illustrates some of these uses by focusing on confidentiality in the context of cryptographic protocols, and in the context of multi-level security systems.

cs.CR↗

arXiv2012

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.

cs.CR↗

arXiv2007

Logic Column 18: Alternative Logics: A Book Review

This article discusses two books on the topic of alternative logics in science: "Deviant Logic", by Susan Haack, and "Alternative Logics: Do Sciences Need Them?", edited by Paul Weingartner.

cs.LO↗

arXiv2007

Characterizing and Reasoning about Probabilistic and Non-Probabilistic Expectation

cs.AI↗

arXiv2007

Dealing With Logical Omniscience: Expressiveness and Pragmatics

We examine four approaches for dealing with the logical omniscience problem and their potential applicability: the syntactic approach, awareness, algorithmic knowledge, and impossible possible worlds. Although in some settings these approaches are equi-expressive and can capture all epistemic states, in other settings of interest (especially with probability in the picture), we show that they are not equi-expressive. We then consider the pragmatics of dealing with logical omniscience-- how to choose an approach and construct an appropriate model.

cs.LO↗

arXiv2006

A Logic for Reasoning about Evidence

We introduce a logic for reasoning about evidence that essentially views evidence as a function from prior beliefs (before making an observation) to posterior beliefs (after making the observation). We provide a sound and complete axiomatization for the logic, and consider the complexity of the decision problem. Although the reasoning in the logic is mainly propositional, we allow variables representing numbers and quantification over them. This expressive power seems necessary to capture important properties of evidence.

cs.AI↗

arXiv2006

Evidence with Uncertain Likelihoods

An agent often has a number of hypotheses, and must choose among them based on observations, or outcomes of experiments. Each of these observations can be viewed as providing evidence for or against various hypotheses. All the attempts to formalize this intuition up to now have assumed that associated with each hypothesis h there is a likelihood function μ_h, which is a probability measure that intuitively describes how likely each observation is, conditional on h being the correct hypothesis. We consider an extension of this framework where there is uncertainty as to which of a number of likelihood functions is appropriate, and discuss how one formal approach to defining evidence, which views evidence as a function from priors to posteriors, can be generalized to accommodate this uncertainty.

cs.AI↗

arXiv2006

Phantom Types and Subtyping

We investigate a technique from the literature, called the phantom-types technique, that uses parametric polymorphism, type constraints, and unification of polymorphic types to model a subtyping hierarchy. Hindley-Milner type systems, such as the one found in Standard ML, can be used to enforce the subtyping relation, at least for first-order values. We show that this technique can be used to encode any finite subtyping hierarchy (including hierarchies arising from multiple interface inheritance). We formally demonstrate the suitability of the phantom-types technique for capturing first-order subtyping by exhibiting a type-preserving translation from a simple calculus with bounded polymorphism to a calculus embodying the type system of SML.

cs.PL↗

arXiv2006

A Formal Foundation for ODRL

ODRL is a popular XML-based language for stating the conditions under which resources can be accessed legitimately. The language is described in English and, as a result, agreements written in ODRL are open to interpretation. To address this problem, we propose a formal semantics for a representative fragment of the language. We use this semantics to determine precisely when a permission is implied by a set of ODRL statements and show that answering such questions is a decidable NP-hard problem. Finally, we define a tractable fragment of ODRL that is also fairly expressive.

cs.LO↗

arXiv2006

Deductive Algorithmic Knowledge

The framework of algorithmic knowledge assumes that agents use algorithms to compute the facts they explicitly know. In many cases of interest, a deductive system, rather than a particular algorithm, captures the formal reasoning used by the agents to compute what they explicitly know. We introduce a logic for reasoning about both implicit and explicit knowledge with the latter defined with respect to a deductive system formalizing a logical theory for agents. The highly structured nature of deductive systems leads to very natural axiomatizations of the resulting logic when interpreted over any fixed deductive system. The decision problem for the logic, in the presence of a single agent, is NP-complete in general, no harder than propositional logic. It remains NP-complete when we fix a deductive system that is decidable in nondeterministic polynomial time. These results extend in a straightforward way to multiple agents.

cs.AI↗

arXiv2005

Probabilistic Algorithmic Knowledge

The framework of algorithmic knowledge assumes that agents use deterministic knowledge algorithms to compute the facts they explicitly know. We extend the framework to allow for randomized knowledge algorithms. We then characterize the information provided by a randomized knowledge algorithm when its answers have some probability of being incorrect. We formalize this information in terms of evidence; a randomized knowledge algorithm returning ``Yes'' to a query about a fact ϕprovides evidence for ϕbeing true. Finally, we discuss the extent to which this evidence can be used as a basis for decisions.

cs.AI↗

arXiv2005

Practical Datatype Specializations with Phantom Types and Recursion Schemes

Datatype specialization is a form of subtyping that captures program invariants on data structures that are expressed using the convenient and intuitive datatype notation. Of particular interest are structural invariants such as well-formedness. We investigate the use of phantom types for describing datatype specializations. We show that it is possible to express statically-checked specializations within the type system of Standard ML. We also show that this can be done in a way that does not lose useful programming facilities such as pattern matching in case expressions.

cs.PL↗

arXiv2005

Logic Column 12: Logical Verification and Equational Verification

This article examines two approaches to verification, one based on using a logic for expressing properties of a system, and one based on showing the system equivalent to a simpler system that obviously has whatever property is of interest. Using examples such as process calculi and regular programs, the relationship between these two approaches is explored.

cs.LO↗