Related papers: Probabilistic Relational Reasoning via Metrics
Firstly in this paper we propose a new criterion function for evaluation of the reductive property about the fuzzy reasoning result for fuzzy modus ponens and fuzzy modus tollens. Secondly unlike fuzzy reasoning methods based on the…
The increasing rise in artificial intelligence has made the use of imprecise language in computer programs like ChatGPT more prominent. Fuzzy logic addresses this form of imprecise language by introducing the concept of fuzzy sets, where…
This paper mainly focuses on (1) a generalized treatment of fuzzy sets of type $n$, where $n$ is an integer larger than or equal to $1$, with an example, mathematical discussions, and real-life interpretation of the given mathematical…
Probabilistic separation logic offers an approach to reasoning about imperative probabilistic programs in which a separating conjunction is used as a mechanism for expressing independence properties. Crucial to the effectiveness of the…
In this paper, we develop compositional methods for formally verifying differential privacy for algorithms whose analysis goes beyond the composition theorem. Our methods are based on the observation that differential privacy has deep…
A key problem in the application of first-order probabilistic methods is the enormous size of graphical models they imply. The size results from the possible worlds that can be generated by a domain of objects and relations. One of the…
Fuzzy modeling has many advantages over the non-fuzzy methods, such as robustness against uncertainties and less sensitivity to the varying dynamics of nonlinear systems. Data-driven fuzzy modeling needs to extract fuzzy rules from the…
Probabilistic programming and the formal analysis of probabilistic algorithms are active areas of research, driven by the widespread use of randomness to improve performance. While functional correctness has seen substantial progress,…
Recent works have shown the power of linear indexed type systems for enforcing complex program properties. These systems combine linear types with a language of type-level indices, allowing more fine-grained analyses. Such systems have been…
Semantic understanding of programs has attracted great attention in the community. Inspired by recent successes of large language models (LLMs) in natural language understanding, tremendous progress has been made by treating programming…
We extend the simply-typed guarded $\lambda$-calculus with discrete probabilities and endow it with a program logic for reasoning about relational properties of guarded probabilistic computations. This provides a framework for programming…
Differential privacy (DP) is a mathematical privacy notion increasingly deployed across government and industry. With DP, privacy protections are probabilistic: they are bounded by the privacy budget parameter, $\epsilon$. Prior work in…
The paper investigates the properties of a fuzzy logic of typicality. The extension of fuzzy logic with a typicality operator was proposed in recent work to define a fuzzy multipreference semantics for Multilayer Perceptrons, by regarding…
We introduce derivative sensitivity, an analogue to local sensitivity for continuous functions. We use this notion in an analysis that determines the amount of noise to be added to the result of a database query in order to obtain a certain…
Several relational program logics have been introduced for integrating reasoning about relational properties of programs and measurement of quantitative difference between computational effects. Towards a general framework for such logics,…
This thesis explores proofs by coupling from the perspective of formal verification. Long employed in probability theory and theoretical computer science, these proofs construct couplings between the output distributions of two…
We study private prediction where differential privacy is achieved by adding noise to the outputs of a non-private model. Existing methods rely on noise proportional to the global sensitivity of the model, often resulting in sub-optimal…
This paper studies the quantitative refinements of Abramsky's applicative similarity and bisimilarity in the context of a generalisation of Fuzz, a call-by-value $\lambda$-calculus with a linear type system that can express programs…
Concern about how to aggregate sensitive user data without compromising individual privacy is a major barrier to greater availability of data. The model of differential privacy has emerged as an accepted model to release sensitive…
Fuzzy relational identification builds a relational model describing systems behaviour by a nonlinear mapping between its variables. In this paper, we propose a new fuzzy relational algorithm based on simplified max-min relational equation.…