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Most interesting proofs in mathematics contain an inductive argument which requires an extension of the LK-calculus to formalize. The most commonly used calculi for induction contain a separate rule or axiom which reduces the valid proof…
A quantum circuit is a computational unit that transforms an input quantum state to an output one. A natural way to reason about its behavior is to compute explicitly the unitary matrix implemented by it. However, when the number of qubits…
The automated proof search system and decidability for logic of correlated knowledge is presented in this paper. The core of the proof system is the sequent calculus with the properties of soundness, completeness, admissibility of cut and…
Just as conventional functional programs may be understood as proofs in an intuitionistic logic, so quantum processes can also be viewed as proofs in a suitable logic. We describe such a logic, the logic of compact closed categories and…
Proof-theoretic methods are developed for subsystems of Johansson's logic obtained by extending the positive fragment of intuitionistic logic with weak negations. These methods are exploited to establish properties of the logical systems.…
Proofs in proof assistants like Rocq can be brittle, breaking easily in response to changes. To address this, recent work introduced an algorithm and tool in Rocq to automatically repair broken proofs in response to changes that correspond…
When considering a sequent-style proof system for quantum programs, there are certain elements of quantum mechanics that we may wish to capture, such as phase, dynamics of unitary transformations, and measurement probabilities. Traditional…
Partial incorrectness logic (partial reverse Hoare logic) has recently been introduced as a new Hoare-style logic that over-approximates the weakest pre-conditions of a program and a post-condition. It is expected to verify systems where…
Reachability Logic is a formalism that can be used, among others, for expressing partial-correctness properties of transition systems. In this paper we present three proof systems for this formalism, all of which are sound and complete and…
Even with impressive advances in automated formal methods, certain problems in system verification and synthesis remain challenging. Examples include the verification of quantitative properties of software involving constraints on timing…
Reasoning methods such as chain-of-thought prompting and self-consistency have shown immense potential to improve the accuracy of large language models across various reasoning tasks. However such methods involve generation of lengthy…
Selective rationalization has become a common mechanism to ensure that predictive models reveal how they use any available features. The selection may be soft or hard, and identifies a subset of input features relevant for prediction. The…
Vision-language models (VLMs) are increasingly deployed in high-stakes settings where reliable uncertainty quantification (UQ) is as important as predictive accuracy. Extended reasoning via chain-of-thought (CoT) prompting or…
We propose a method for learning cyclic causal models from a combination of observational and interventional equilibrium data. Novel aspects of the proposed method are its ability to work with continuous data (without assuming linearity)…
We advocate here the use of computational logic for systems biology, as a \emph{unified and safe} framework well suited for both modeling the dynamic behaviour of biological systems, expressing properties of them, and verifying these…
Human conversation relies heavily on conversational implicature, in which speakers convey meanings that are suggested rather than explicitly stated. Although recent large language models exhibit strong conversational fluency, they remain…
We investigate here a new version of the Calculus of Inductive Constructions (CIC) on which the proof assistant Coq is based: the Calculus of Congruent Inductive Constructions, which truly extends CIC by building in arbitrary first-order…
Mechanized verification of liveness properties for infinite programs with effects and nondeterminism is challenging. Existing temporal reasoning frameworks operate at the level of models such as traces and automata. Reasoning happens at a…
Chase algorithms are indispensable in the domain of knowledge base querying, which enable the extraction of implicit knowledge from a given database via applications of rules from a given ontology. Such algorithms have proved beneficial in…
We design a proof system for propositional classical logic that integrates two languages for Boolean functions: standard conjunction-disjunction-negation and binary decision trees. We give two reasons to do so. The first is…