Related papers: From Qualitative to Quantitative Proofs of Securit…
We consider the problem of counting the number of answers to a first-order formula on a finite structure. We present and study an extension of first-order logic in which algorithms for this counting problem can be naturally and conveniently…
Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order…
We present an iterative algorithm for enforcing policies represented in a first-order logic, which can, in particular, express all transmission-related clauses in the HIPAA Privacy Rule. The logic has three features that raise challenges…
Vardanyan's Theorems state that $\mathsf{QPL}(\mathsf{PA})$ - the quantified provability logic of Peano Arithmetic - is $\Pi^0_2$ complete, and in particular that this already holds when the language is restricted to a single unary…
In this paper we propose a general approach to define a many-valued preferential interpretation of gradual argumentation semantics. The approach allows for conditional reasoning over arguments and boolean combination of arguments, with…
We delineate a methodology for the specification and verification of flow security properties expressible in the opacity framework. We propose a logic, OpacTL , for straightforwardly expressing such properties in systems that can be…
In this note, we observe that quantum logspace computations are verifiable by classical logspace algorithms, with unconditional security. More precisely, every language in BQL has an (information-theoretically secure) streaming proof with a…
Nominal logic is a variant of first-order logic that provides support for reasoning about bound names in abstract syntax. A key feature of nominal logic is the new-quantifier, which quantifies over fresh names (names not appearing in any…
Equational reasoning with string diagrams provides an intuitive means of proving equations between morphisms in a symmetric monoidal category. This can be extended to proofs of infinite families of equations using a simple graphical syntax…
Formal verification provides strong guarantees of correctness of software, which are especially important in safety or security critical systems. Hoare logic is a widely used formalism for rigorous verification of software against…
This paper provides two extensions of first order logic by `$\omega$-rules'. In each case we characterize the countable structures whose theory in the logic is categorical (has a unique model). In the one-sorted inferential $\omega$-logic,…
Probability Quantification (PQ) predictions of the efficacy of safety-critical protective systems is challenging. Yet, the popularity of PQ methodologies (e.g., Probabilistic Risk Assessment (PRA), Quantitative Risk Analysis (QRA) and…
For an $n\times n$ random image with independent pixels, black with probability $p(n)$ and white with probability $1-p(n)$, the probability of satisfying any given first-order sentence tends to 0 or 1, provided both $p(n)n^{\frac{2}{k}}$…
We introduce an extension of first-order logic that comes equipped with additional predicates for reasoning about an abstract state. Sequents in the logic comprise a main formula together with pre- and postconditions in the style of Hoare…
This paper considers the complexity and properties of KLM-style preferential reasoning in the setting of propositional logic with team semantics and dependence atoms, also known as propositional dependence logic. Preferential team-based…
Measuring how quickly iterative methods converge is essential in computational mathematics, but current approaches have significant limitations. Q-order analysis requires strict smoothness conditions, while R-order analysis lacks precision…
Primal logic arose in access control; it has a remarkably efficient (linear time) decision procedure for its entailment problem. But primal logic is a general logic of information. In the realm of arbitrary items of information (infons),…
We extend first-order logic to include variadic function symbols, and prove a substitution lemma. Two applications are given: one to bounded quantifier elimination and one to the definability of certain Borel sets.
Natural language understanding applications such as interactive planning and face-to-face translation require extensive inferencing. Many of these inferences are based on the meaning of particular open class words. Providing a…
Quantitative aspects of computation are related to the use of both physical and mathematical quantities, including time, performance metrics, probability, and measures for reliability and security. They are essential in characterizing the…