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Neural network design has utilized flexible nonlinear processes which can mimic biological systems, but has suffered from a lack of traceability in the resulting network. Graphical probabilistic models ground network design in probabilistic…
Adjoint logic is a general approach to combining multiple logics with different structural properties, including linear, affine, strict, and (ordinary) intuitionistic logics, where each proposition has an intrinsic mode of truth. It has…
This paper studies the connection between probabilistic conditional independence in uncertain reasoning and data dependency in relational databases. As a demonstration of the usefulness of this preliminary investigation, an alternate proof…
We consider the problem of automatically verifying programs which manipulate arbitrary data structures. Our specification language is expressive, contains a notion of \emph{separation}, and thus enables a precise specification of…
This paper presents PFLP, a library for probabilistic programming in the functional logic programming language Curry. It demonstrates how the concepts of a functional logic programming language support the implementation of a library for…
Matching logic is a logical framework for specifying and reasoning about programs using pattern matching semantics. A pattern is made up of a number of structural components and constraints. Structural components are syntactically matched,…
Probabilistic logic programs are logic programs where some facts hold with a specified probability. Here, we investigate these programs with a causal framework that allows counterfactual queries. Learning the program structure from…
We propose a sound and complete proof rule ProbTA for quantitative analysis of violation probability of probabilistic programs. Our approach extends the technique of trace abstraction with probability in the control-flow randomness style,…
To address the increasing size and complexity of modern software systems, compositional verification separates the verification of single components from the verification of their composition. In architecture-based verification, the former…
Dependency pairs are one of the most powerful techniques to analyze termination of term rewrite systems (TRSs) automatically. We adapt the dependency pair framework to the probabilistic setting in order to prove almost-sure innermost…
Quantitative separation logic (QSL) is an extension of separation logic (SL) for the verification of probabilistic pointer programs. In QSL, formulae evaluate to real numbers instead of truth values, e.g., the probability of memory-safe…
Lighthouse projects such as CompCert, seL4, IronFleet, and DeepSpec have demonstrated that full verification of entire systems is feasible by establishing a refinement relation between an abstract system specification and an executable…
Bayesian probabilistic programming languages (BPPLs) let users denote statistical models as code while the interpreter infers the posterior distribution. The semantics of BPPLs are usually mathematically complex and unable to reason about…
Current approaches for formal verification of algorithms face important limitations. For specification, they cannot express algorithms naturally and concisely, especially for algorithms with states and flexible control flow. For…
Recent work on loglinear models in probabilistic constraint logic programming is applied to first-order probabilistic reasoning. Probabilities are defined directly on the proofs of atomic formulae, and by marginalisation on the atomic…
Experimental tests of Bell's inequality allow to distinguish quantum mechanics from local hidden variable theories. Such tests are performed by measuring correlations of two entangled particles (e.g. polarization of photons or spins of…
Verifying mathematical proofs is difficult, but can be automated with the assistance of a computer. Autoformalization is the task of automatically translating natural language mathematics into a formal language that can be verified by a…
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.…
We introduce a model of probabilistic verification in mechanism design. The principal elicits a message from the agent and then selects a test to give the agent. The agent's true type determines the probability with which he can pass each…
The emergence of tools based on artificial intelligence has also led to the need of producing explanations which are understandable by a human being. In most approaches, the system is considered a black box, making it difficult to generate…