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While supporting the execution of business processes, information systems record event logs. Conformance checking relies on these logs to analyze whether the recorded behavior of a process conforms to the behavior of a normative…
A reliable method for characterizing quantum operations that is suitable for improving and validating their accuracies is indispensable for realizing a practical quantum computer. Known methods are still not sufficient because they lack…
There are termination proofs that are produced by termination tools for which certifiers are not powerful enough. However, a similar situation also occurs in the other direction. We have formalized termination techniques in a more general…
SMT-based program analysis and verification often involve reasoning about program features that have been specified using quantifiers; incorporating quantifiers into SMT-based reasoning is, however, known to be challenging. If quantifier…
Over the past few decades, combinatorial solvers have seen remarkable performance improvements, enabling their practical use in real-world applications. In some of these applications, ensuring the correctness of the solver's output is…
Higher-order rewriting is a framework in which one can write higher-order programs and study their properties. One such property is termination: the situation that for all inputs, the program eventually halts its execution and produces an…
Answering logical queries over incomplete knowledge bases is challenging because: 1) it calls for implicit link prediction, and 2) brute force answering of existential first-order logic queries is exponential in the number of existential…
Logically constrained term rewriting is a relatively new formalism where rules are equipped with constraints over some arbitrary theory. Although there are many recent advances with respect to rewriting induction, completion, complexity…
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…
Program completion is a translation from the language of logic programs into the language of first-order theories. Its original definition has been extended to programs that include integer arithmetic, accept input, and distinguish between…
It has been argued that reduction procedures are closely connected to the question about identity of proofs and that accepting certain reductions would lead to a trivialization of identity of proofs in the sense that every derivation of the…
Formal verification of complex algorithms is challenging. Verifying their implementations goes beyond the state of the art of current automatic verification tools and usually involves intricate mathematical theorems. Certifying algorithms…
In this paper, we present the Logically submissions to De-Factify 2 challenge (DE-FACTIFY 2023) on the task 1 of Multi-Modal Fact Checking. We describes our submissions to this challenge including explored evidence retrieval and selection…
Software system certification presents itself with many challenges, including the necessity to certify the system at the level of functional requirements, code and binary levels, the need to chase down run-time errors, and the need for…
Partial correctness of imperative or functional programming divides in logic programming into two notions. Correctness means that all answers of the program are compatible with the specification. Completeness means that the program produces…
We consider Proof Complexity in light of the unusual binary encoding of certain combinatorial principles. We contrast this Proof Complexity with the normal unary encoding in several refutation systems, based on Resolution and Integer Linear…
Convex functions of quantum states play a key role in quantum physics, with examples ranging from Bell inequalities to von Neumann entropy. However, in experimental scenarios, direct measurements of these functions are often impractical. We…
We propose a new cyclic proof system for automated, equational reasoning about the behaviour of pure functional programs. The key to the system is the way in which cyclic proof and equational reasoning are mediated by the use of contextual…
This note formally defines the concept of coinductive validity of judgements, and contrasts it with inductive validity. For both notions it shows how a judgement is valid iff it has a formal proof. Finally, it defines and illustrates the…
The safety of automated driving systems must be justified by convincing arguments and supported by compelling evidence to persuade certification agencies, regulatory entities, and the general public to allow the systems on public roads.…