Browsing by Author "Kulicki, Piotr"

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    Aristotle's Syllogistic as a Deductive System
    (MDPI, 2020-05-19) Kulicki, Piotr
    Aristotle's syllogistic is the first ever deductive system. After centuries, Aristotle's ideas are still interesting for logicians who develop Aristotle's work and draw inspiration from his results and even more from his methods. In the paper we discuss the essential elements of the Aristotelian system of syllogistic and Łukasiewicz's reconstruction of it based on the tools of modern formal logic. We pay special attention to the notion of completeness of a deductive system as discussed by both authors. We describe in detail how completeness can be defined and proved with the use of an axiomatic refutation system. Finally, we apply this methodology to different axiomatizations of syllogistic presented by Łukasiewicz, Lemmon and Shepherdson.
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    Towards Quantum-Secured Permissioned Blockchain: Signature, Consensus, and Logic
    (MDPI, 2019-09-12) Sun, Xin; Sopek, Mirek; Wang, Qauanlong; Kulicki, Piotr
    While Blockchain technology is universally considered as a significant technology for the near future, some of its pillars are under a threat of another thriving technology, Quantum Computing. In this paper, we propose important safeguard measures against this threat by developing a framework of a quantum-secured, permissioned blockchain called Logicontract (LC). LC adopts a digital signature scheme based on Quantum Key Distribution (QKD) mechanisms and a vote-based consensus algorithm to achieve consensus on the blockchain. The main contribution of this paper is in the development of: (1) unconditionally secure signature scheme for LC which makes it immune to the attack of quantum computers; (2) scalable consensus protocol used by LC; (3) logic-based scripting language for the creation of smart contracts on LC; (4) quantum-resistant lottery protocol which illustrates the power and usage of LC.