Related papers: From Qualitative to Quantitative Proofs of Securit…

First-order logic has been established as an important tool for modeling and verifying intricate systems such as distributed protocols and concurrent systems. These systems are parametric in the number of nodes in the network or the number…

We provide a denotational semantics for first-order logic that captures the two-level view of the computation process typical for constraint programming. At one level we have the usual program execution. At the other level an automatic…

We will investigate proof-theoretic and linguistic aspects of first-order linear logic. We will show that adding partial order constraints in such a way that each sequent defines a unique linear order on the antecedent formulas of a sequent…

We present a formal logic for quantitative reasoning about security properties of network protocols. The system allows us to derive concrete security bounds that can be used to choose key lengths and other security parameters. We provide…

A policy describes the conditions under which an action is permitted or forbidden. We show that a fragment of (multi-sorted) first-order logic can be used to represent and reason about policies. Because we use first-order logic, policies…

Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…

Conditional logics play an important role in recent attempts to formulate theories of default reasoning. This paper investigates first-order conditional logic. We show that, as for first-order probabilistic logic, it is important not to…

Qualitative and quantitative approaches to reasoning about uncertainty can lead to different logical systems for formalizing such reasoning, even when the language for expressing uncertainty is the same. In the case of reasoning about…

Semi-algebraic proof systems such as sum-of-squares (SoS) have attracted a lot of attention recently due to their relation to approximation algorithms: constant degree semi-algebraic proofs lead to conjecturally optimal polynomial-time…

We consider the problem of answering queries about formulas of first-order logic based on background knowledge partially represented explicitly as other formulas, and partially represented as examples independently drawn from a fixed…

In this paper we consider the specification and verification of infinite-state systems using temporal logic. In particular, we describe parameterised systems using a new variety of first-order temporal logic that is both powerful enough for…

We present a new system S for handling uncertainty in a quantified modal logic (first-order modal logic). The system is based on both probability theory and proof theory. The system is derived from Chisholm's epistemology. We concretize…

First-order optimization methods have attracted a lot of attention due to their practical success in many applications, including in machine learning. Obtaining convergence guarantees and worst-case performance certificates for first-order…

A probabilistic propositional logic, endowed with an epistemic component for asserting (non-)compatibility of diagonizable and bounded observables, is presented and illustrated for reasoning about the random results of projective…

We develop a characterization of quantum states by means of first order variables and random variables, within a predicative logic with equality, in the framework of basic logic and its definitory equations. We introduce the notion of…

Permissive-Nominal Logic (PNL) is an extension of first-order predicate logic in which term-formers can bind names in their arguments. This allows for direct axiomatisations with binders, such as of the lambda-binder of the lambda-calculus…

Blocked clauses provide the basis for powerful reasoning techniques used in SAT, QBF, and DQBF solving. Their definition, which relies on a simple syntactic criterion, guarantees that they are both redundant and easy to find. In this paper,…

First-order logic is the basis for many knowledge representation formalisms and methods. Providing technological support for learning to write first-order formulas for natural language specifications requires methods to test formulas for…

A new logic for verification of security policies is proposed. The logic, HyperLTL, extends linear-time temporal logic (LTL) with connectives for explicit and simultaneous quantification over multiple execution paths, thereby enabling…

Verifying software correctness has always been an important and complicated task. Recently, formal proofs of critical properties of algorithms and even implementations are becoming practical. Currently, the most powerful automated proof…