Related papers: Combining Classical and Probabilistic Independence…
Probabilistic programming is the idea of writing models from statistics and machine learning using program notations and reasoning about these models using generic inference engines. Recently its combination with deep learning has been…
We investigate the formal semantics of a simple imperative language that has both classical and quantum constructs. More specifically, we provide an operational semantics, a denotational semantics and two Hoare-style proof systems: an…
Understanding the behavior of learned classifiers is an important task, and various black-box explanations, logical reasoning approaches, and model-specific methods have been proposed. In this paper, we introduce probabilistic sufficient…
Integrated circuit (IC) piracy and overproduction are serious issues that threaten the security and integrity of a system. Logic locking is a type of hardware obfuscation technique where additional key gates are inserted into the circuit.…
Automated planning is a major topic of research in artificial intelligence, and enjoys a long and distinguished history. The classical paradigm assumes a distinguished initial state, comprised of a set of facts, and is defined over a set of…
This thesis focuses on advancing probabilistic logic programming (PLP), which combines probability theory for uncertainty and logic programming for relations. The thesis aims to extend PLP to support both discrete and continuous random…
Relational Hoare logics (RHL) provide rules for reasoning about relations between programs. Several RHLs include a rule we call sequential product that infers a relational correctness judgment from judgments of ordinary Hoare logic (HL).…
On the one hand, ordered completion is a fundamental technique in equational theorem proving that is employed by automated tools. On the other hand, their complexity makes such tools inherently error prone. As a remedy to this situation we…
We present the Polar framework for fully automating the analysis of classical and probabilistic loops using algebraic reasoning. The central theme in Polar comes with handling algebraic recurrences that precisely capture the loop semantics.…
Classical probability theory is formulated using sets. In this paper, we extend classical probability theory with propositional computability logic. Unlike other formalisms, computability logic is built on the notion of events/games, which…
Verifying whether a procedure is observationally pure is useful in many software engineering scenarios. An observationally pure procedure always returns the same value for the same argument, and thus mimics a mathematical function. The…
We introduce a new theorem prover for classical higher-order logic named auto2. The prover is designed to make use of human-specified heuristics when searching for proofs. The core algorithm is a best-first search through the space of…
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 examine the relationships between axiomatic and cyclic proof systems for the partial and total versions of Hoare logic and those of its dual, known as reverse Hoare logic (or sometimes incorrectness logic). In the axiomatic proof systems…
Formal verification of strategic abilities is a hard problem. We propose to use the methodology of assume-guarantee reasoning in order to facilitate model checking of alternating-time temporal logic with imperfect information and imperfect…
Realizing flow security in a concurrent environment is extremely challenging, primarily due to non-deterministic nature of execution. The difficulty is further exacerbated from a security angle if sequential threads disclose control…
A reliable technique for deductive program verification should be proven sound with respect to the semantics of the programming language. For each different language, the construction of a separate soundness proof is often a laborious…
In spite of the rapidly increasing number of applications of machine learning in various domains, a principled and systematic approach to the incorporation of domain knowledge in the engineering process is still lacking and ad hoc solutions…
Uniform proofs are sequent calculus proofs with the following characteristic: the last step in the derivation of a complex formula at any stage in the proof is always the introduction of the top-level logical symbol of that formula. We…
Dependent type theory gives an expressive type system facilitating succinct formalizations of mathematical concepts. In practice, it is mainly used for interactive theorem proving with intensional type theories, with PVS being a notable…