Based on ideas of quantum theory of open systems and psychological dual system theory we propose two novel versions of Non-Boolean logic. The first version can be interpreted in our opinion as simplified description of primitive (mythological) thinking and the second one as the toy model of everyday human reasoning in which aside from logical deduction, heuristic elements and beliefs also play ...

Superdeduction is a formalism closely related to deduction modulo which permits to enrich a first-order deduction system—such as natural deduction or sequent calculus— with new inference rules automatically computed from the presentation of a theory. We give a natural encoding from every Pure Type System (PTS) into superdeduction by defining an appropriate first-order theory. We prove that this...

With the impact of urbanization and other factors, vernacular architectural heritage faces problem how to carry on innovate for sustainable development with originality authenticity in process redesigning planning. Therefore, this study uses visualization method quantitative analysis analyze research trends hot spots domestic architecture explore new ways coexistence between architecture, subje...

It is believed in the West that logic began with Aristotle, and that logic is universal. The core of Western thought—including present-day formal mathematics and the philosophy of science—is premised on the belief that logical truths are universal, that they are necessary truths, and that logical deduction is certain and infallible. These beliefs about logic however are untenable, both historic...

We discuss the general concept of calculational reasoning within Isabelle/Isar, which provides a framework for high-level natural deduction proofs that may be written in a human-readable fashion. Setting out from a few basic logical concepts of the underlying meta-logical framework of Isabelle, such as higher-order unification and resolution, calculational commands are added to the basic Isar p...

Business Processes for Web Services are the new paradigm for the lightweight integration of business from different enterprises. Yet, there is not a comprehensive proposal for a logical framework for access control for business processes though logics for access control policies for basic web services are well studied. In this paper we propose a logical framework for reasoning (deduction, abduc...

A logical framework consisting of a polymorphic call-byvalue functional language and a first-order logic on the values is presented, which is a reconstruction of the logic of the verification system VeriFun. The reconstruction uses contextual semantics to define the logical value of equations. It equates undefinedness and nontermination, which is a standard semantical approach. The main results...

We describe a collaborative effort in which the HOL4 theorem prover is being used to formally verify properties of a structure within the Large Hadron Collider (LHC) machine protection system at the European Organization for Nuclear Research (CERN). This structure, known as Successive Running Sums (SRS), generates the primary input to the decision logic that must initiate a critical action by t...

Deduction Modulo implements Poincaré’s principle by identifying deduction and computation as different paradigms and making their interaction possible. This leads to logical systems like the sequent calculus or natural deduction modulo. Even if deduction modulo is logically equivalent to first-order logic, proofs in such systems are quite different and dramatically simpler with one cost: cut el...