We develop a sound and complete equational theory for the functional quantum programming language QML. The soundness and completeness of the theory are with respect to the previously developed denotational semantics of QML. The completeness proof also gives rise to a normalisation algorithm following the normalisation-by-evaluation approach. The current work focuses on the pure fragment of QML,...

Current approaches for proving the correctness of business processes focus on either soundness, weak soundness, or relaxed soundness. Soundness states that each activity should be on a path from the initial to the final activity, that after the final activity has been reached no other activities should become active, and that there are no unreachable activities. Relaxed soundness softens soundn...

For a suitable collection D of small categories, we define the D-accessible categories, generalizing the λ-accessible categories of Lair, Makkai, and Paré; here the λ-accessible categories are seen as the D-accessible categories where D consists of the λ-small categories. A small category C is called D-filtered when C-colimits commute with D-limits in the category of sets. An object of a catego...

Citation: Hing ML, Klanten OS, Dowton M and Wong MYL (2017) The Right Tools for the Job: Cooperative Breeding Theory and an Evaluation of the Methodological Approaches to Understanding the Evolution and Maintenance of Sociality. Front. Ecol. Evol. 5:100. doi: 10.3389/fevo.2017.00100 The Right Tools for the Job: Cooperative Breeding Theory and an Evaluation of the Methodological Approaches to Un...

We present ‘Ribbon Proofs’, a graphical proof system for the Logic of Bunched Implications (BI). We give the informal, graphical, notation, we formalise the system algebraically and sketch the proof of its soundness and completeness. We discuss the spatial and geometrical nature of the proof system and its relation to BI’s spatial model theory.

We present a Hilbert-style axiomatization of a paraconsistent logic, called G3, recently introduced. G ′ 3 is based on a 3-valued semantics. We prove a soundness and completeness theorem. The replacement theorem holds in G3. As it has already been shown in previous work, G ′ 3 can express some nonmonotonic semantics.

Charles R. Henderson was proud to be a product of a farm in Page County, Iowa. He was a one man track team in Coin, Iowa, and a brilliant student. He became a world class competitor in track at Iowa State College and, at the same time, compiled a top academic record. His early experiences set the stage for the exceptional contributions of his animal breeding career, which did not begin until he...

We give formulations for modal deductive databases and present a modal query language called MDatalog. We define modal relational algebras and give the seminaive evaluation algorithm, the top-down evaluation algorithm, and the magic-set transformation for MDatalog queries. The results of this paper like soundness and completeness of the top-down evaluation algorithm or correctness of the magic-...

We give formulations for modal deductive databases and present a modal query language called MDatalog. We define modal relational algebras and give the seminaive evaluation algorithm, the top-down evaluation algorithm, and the magic-set transformation for MDatalog queries. The results of this paper like soundness and completeness of the top-down evaluation algorithm or correctness of the magic-...