Related papers: Foundations of logic programming in hybrid-dynamic…
Traditional cognitive science rests on a foundation of classical logic and probability theory. This foundation has been seriously challenged by several findings in experimental psychology on human decision making. Meanwhile, the formalism…
In prior work, we showed that logic programming compilation can be given a proof-theoretic justification for generic abstract logic programming languages, and demonstrated this technique in the case of hereditary Harrop formulas and their…
We present a logical calculus for reasoning about information flow in quantum programs. In particular we introduce a dynamic logic that is capable of dealing with quantum measurements, unitary evolutions and entanglements in compound…
A first-order logic with quantum variables is needed as an assertion language for specifying and reasoning about various properties (e.g. correctness) of quantum programs. Surprisingly, such a logic is missing in the literature, and the…
Modal logic is a paradigm for several useful and applicable formal systems in computer science. It generally retains the low complexity of classical propositional logic, but notable exceptions exist in the domains of description, temporal,…
Most modern (classical) programming languages support recursion. Recursion has also been successfully applied to the design of several quantum algorithms and introduced in a couple of quantum programming languages. So, it can be expected…
Motivated by applications in modelling quantum systems using coalgebraic techniques, we introduce a fibred coalgebraic logic. Our approach extends the conventional predicate lifting semantics with additional modalities relating conditions…
A general framework is proposed for integration of rules and external first order theories. It is based on the well-founded semantics of normal logic programs and inspired by ideas of Constraint Logic Programming (CLP) and constructive…
We present a logical separability analysis for a functional quantum computation language. This logic is inspired by previous works on logical analysis of aliasing for imperative functional programs. Both analyses share similarities notably…
The emphasis is made on the juxtaposition of (quantum~theorem) proving versus quantum (theorem~proving). The logical contents of verification of the statements concerning quantum systems is outlined. The Zittereingang (trembling input)…
An algorithm for computing the stable model semantics of logic programs is developed. It is shown that one can extend the semantics and the algorithm to handle new and more expressive types of rules. Emphasis is placed on the use of…
A semantic embedding of (constant domain) quantified conditional logic in classical higher-order logic is presented.
The rapid progress of computer technology has been accompanied by a corresponding evolution of software development, from hardwired components and binary machine code to high level programming languages, which allowed to master the…
Part of the theory of logic programming and nonmonotonic reasoning concerns the study of fixed-point semantics for these paradigms. Several different semantics have been proposed during the last two decades, and some have been more…
The syntactic nature of logic and computation separates them from other fields of mathematics. Nevertheless, syntax has been the only way to adequately capture the dynamics of proofs and programs such as cut-elimination, and the finiteness…
This paper summarises the results obtained by the author and his collaborators in a program logic approach to the verification of quantum programs, including quantum Hoare logic, invariant generation and termination analysis for quantum…
Rule-based reasoning is an essential part of human intelligence prominently formalized in artificial intelligence research via logic programs. Describing complex objects as the composition of elementary ones is a common strategy in computer…
Hybrid programs combine digital control with differential equations, and naturally appear in a wide range of application domains, from biology and control theory to real-time software engineering. The entanglement of discrete and continuous…
We introduce an extension of first-order logic that comes equipped with additional predicates for reasoning about an abstract state. Sequents in the logic comprise a main formula together with pre- and postconditions in the style of Hoare…
Hybrid computation combines discrete and continuous dynamics in the form of an entangled mixture inherently present both in various natural phenomena, and in applications ranging from control theory to microbiology. The emergent behaviours…