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A modified authentication approach for cloud computing in e-healthcare systems
Published in Sabyasachi Pramanik, Anand Sharma, Surbhi Bhatia, Dac-Nhuong Le, An Interdisciplinary Approach to Modern Network Security, 2022
The method of authentication implements a challenge-response protocol that shows the identity of the end-user. We use the Schnorr zero-knowledge identification protocol [24] as a challenge-response method. However, other zero-knowledge identification protocols are also possible [25]. We used the Schnorr protocol to satisfy the three properties of completeness, soundness, and zero-knowledge [26]. The completeness property is a condition for a statement’s validity so that if a statement is valid, it would assure an honest verifier of its truth. They considered the soundness property, the probability that an honest prover would be convinced that a false statement is true. The zero-knowledge property guarantees that no additional information can be obtained by a verifier [27].
First-order logic
Published in Richard E. Neapolitan, Xia Jiang, Artificial Intelligence, 2018
Richard E. Neapolitan, Xia Jiang
Similar to propositional logic, in first-order logic an argument consists of a set of formulas, called the premises, and a formula called the conclusion. We say that the premises entail the conclusion if in every model in which all the premises are true, the conclusion is also true. If the premises entail the conclusion, we say the argument is sound; otherwise we say it is a fallacy. A set of inference rules is called a deduction system. A deduction system is sound if it only derives sound arguments. A deduction system is complete if it can derive every sound argument. Gödel’s famous first incompleteness theorem proves that in general there is no complete deduction system in first-order logic. However, its discussion is beyond the scope of this text. Briefly, Gödel showed that there are statements about the natural numbers that cannot be proved.
Logic
Published in Jay Liebowitz, The Handbook of Applied Expert Systems, 2019
The semantics of classical logic assigns meaning to the formulae by defining a mapping between the symbols of the formula and the objects and relationships of the world. This mapping is called an interpretation. An interpretation consists of a domain and a mapping from elements, functions, and relations of the domain to constant, variables, function, and predicate symbols in the formula. Constants, variables, and terms denote elements of the domain. A formula can take the values true or false. A model M is an interpretation that makes a formula α true and is denoted: M = α, which is read “M satisfies α.” A formula α is valid if it is true for every interpretation, and denoted by =α. A formula is satisfiable if it has a model, and is a contradiction if it is false for every interpretation. A set of formulae Γ is satisfiable if there is an interpretation that satisfies every formula in Γ. The fact that every interpretation that satisfies a set of formulae Γ also satisfies a formula a, is denoted by Γ=α and read “Γ logically implies α.” A proof procedure (or calculus) consists of a set of axioms, and a set of rules of inference for deductive reasoning. A formula α which is derived from the axioms by a sequence of inference rules applications is called a theorem and is denoted by: 〈α. If α is derived from a set of formulae Γ, we write Γ 〈 a, which is read α is deduced from Γ. Soundness and completeness are two attributes of a proof procedure with respect to semantics. Soundness means that any theorem deduced by the proof procedure is valid. Completeness means that any valid formula can be proved by the proof procedure. The completeness theorem establishes the relationship between deduction and logical implication:
Grounding rules for (relevant) implication
Published in Journal of Applied Non-Classical Logics, 2021
As explained by Dunn and Restall (2002), the system R has both an algebraic semantics and a frame-semantics. The former has been introduced by Dunn (1970), while the latter has been developed by Fine (1974); Urquhart (1972) and Routley and Meyer (1973). Routley and Meyer's approach is probably the most well-known (see Mares, 2014) and it is based on the idea of interpreting the implication connective by means of a ternary relation Rijz such that if, and only if, ∈W (if Rijz and , then ). In this approach, while the connectives of conjunction and disjunction are treated classically, the negation connective is treated by an unary operation + on worlds,7 such that for each world i, there is a world , i ⊧ if, and only if, .8 By denoting with the class of relevant frames of Routley and Meyer (1973), the soundness and completeness theorem is provable for the logic (Figure 1) .
A Dynamic User Interface Based BCI Environmental Control System
Published in International Journal of Human–Computer Interaction, 2020
Saisai Zhong, Yadong Liu, Yang Yu, Jingsheng Tang, Zongtan Zhou, Dewen Hu
Compared with previous BCI systems that were combined with AR technology (Kansaku et al., 2010; Otsuka et al., 2015), the proposed system is an integrated system with multiple devices. In particular, the proposed system includes a wheelchair, which can satisfy the subject’s requirement for movement. Besides, with AR technology, the proposed system develops a dynamic UI. The dynamic UI generates the control options based on the real-time scene. This helps to assist the subject to select the desired control object from multiple devices. Compared with the method of presenting commands as soon as the object was detected, the proposed system give the subject more autonomy. Therefore, in terms of functional completeness and the interactive design, the proposed system has some advantages.
Natural implicative expansions of variants of Kleene's strong 3-valued logic with Gödel-type and dual Gödel-type negation
Published in Journal of Applied Non-Classical Logics, 2021
The paper is organised as follows. In § 2, the matrices MK3 and MK3 are defined and the 6 natural implicative expansions of MK3 and the 24 expanding MK3 are displayed. In § 3, the matrix semantics corresponding to each one of these 30 natural implicative expansions is translated into an overdetermined BD-semantics (expansions of MK3) and an underdetermined BD-semantics (expansions of MK3). Also, the soundness and completeness proofs are sketched. We follow the strategy set up in Brady (1982) and just as it is particularly applied in Robles and Méndez (2019) and Robles et al. (2019), as pointed out above. Thus, it will not be necessary to go down to each detail and many of the proofs will be referred to our papers (Robles & Méndez, 2019; Robles et al., 2019). In § 4, the logics determined by the 30 natural implicative expansions are defined and the soundness and completeness theorems are proved. Soundness is proved w.r.t. the matrix semantics, and completeness w.r.t. the BD-semantics corresponding to each logic. Given the equivalence in each case between the matrix semantics and the BD-semantics, we have soundness and completeness w.r.t. both types of semantics. In § 5, we prove some interesting properties predicable of the logics defined in § 4, and finally, the paper is ended in § 6 with some remarks on the results obtained.