Multi-Valued Logics

Panti, Giovanni

doi:10.1007/978-94-017-1735-9_2

Cited by 13 publications

(7 citation statements)

References 70 publications

(92 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…82 See also Panti [209], p.48, §2.5.1 Bochvar's and Kleene's systems: "In addition to 0 and 1 for false and true, they have a third value 2. While for Łukasiewicz the third value stands for possible, or not yet detennined, from Bochvar's point of view it stands for paradoxical, or meaningless.…”

Section: Ex Contradictione Quodlibet (Ecq)mentioning

confidence: 99%

See 1 more Smart Citation

Analytic Continuation of $ζ(s)$ Violates the Law of Non-Contradiction (LNC)

Sharon

2018

Preprint

View full text Add to dashboard Cite

The Dirichlet series of ζ(s) was long ago proven to be divergent throughout half-plane Re(s) ≤ 1. If also Riemann's proposition is true, that there exists an "expression" of ζ(s) that is convergent at all s (except at s = 1), then ζ(s) is both divergent and convergent throughout half-plane Re(s) ≤ 1 (except at s = 1).This result violates all three of Aristotle's "Laws of Thought": the Law of Identity (LOI), the Law of the Excluded Middle (LEM), and the Law of Non-Contradition (LNC). In classical and intuitionistic logics, the violation of LNC also triggers the "Principle of Explosion" / Ex Contradictione Quodlibet (ECQ).In addition, the Hankel contour used in Riemann's analytic continuation of ζ(s) violates Cauchy's integral theorem, providing another proof of the invalidity of Riemann's ζ(s). Riemann's ζ(s) is one of the L-functions, which are all invalid due to analytic continuation. This result renders unsound all theorems (e.g. Modularity, Fermat's last) and conjectures (e.g. BSD, Tate, Hodge, Yang-Mills) that assume that an L-function (e.g. Riemann's ζ(s)) is valid.We also show that the Riemann Hypothesis (RH) is not "non-trivially true" in classical logic, intuitionistic logic, or three-valued logics (3VLs) that assign a third truth-value to paradoxes (Bochvar's 3VL, Priest's LP ).

show abstract

Section: Ex Contradictione Quodlibet (Ecq)mentioning

confidence: 99%

“…] Also Langer [171] reaffirms these comments (emphasis added in bold font. Italic font is in the original): 209 The same theorem may follow from more than one possible selection of premises ... But contradictory theorems can never follow from consistent postulates.…”

Section: Lnc Is the Test For Consistency Of An Axiomatic Systemmentioning

confidence: 99%

Analytic Continuation of $ζ(s)$ Violates the Law of Non-Contradiction (LNC)

Sharon

2018

Preprint

View full text Add to dashboard Cite

show abstract

“…This issue is well known from primitive recursive function theory. The formal definition of the emptiness test is based on the Kleene's system of "strong connectives" [31]. 3 The corresponding operations of the three valued logic are negation ¬ 3 , disjunction ∨ 3 , and conjunction ∧ 3 .…”

Section: Emptiness Test Of Annotated Dfamentioning

confidence: 99%

Matchmaking for business processes based on choreographies

Wombacher¹,

Fankhauser²,

Mahleko³

et al. 2004

IEEE International Conference on E-Technology, E-Commerce and E-Service, 2004. EEE '04. 2004

110

View full text Add to dashboard Cite

Web services have a potential to enhance B2B ecommerce over the Internet by allowing companies and organizations to publish their business processes on service directories where potential trading partners can find them. This can give rise to new business paradigms based on ad-hoc trading relations as companies, particularly small to medium scale, can cheaply and flexibly enter into fruitful contracts, e.g., through subcontracting from big companies by simply publishing their business processes and the services they offer. More business process support by the web service infrastructure is however needed before such a paradigm change can materialize. A service for searching and matchmaking of business processes does not yet exist in the current infrastructure. We believe that such a service is needed and will enable companies and organizations to be able to establish ad-hoc business relations without relying on manually negotiated interorganizational workflows. This paper gives a formal semantics to business process matchmaking based on finite state automata extended by logical expressions associated to states.

show abstract

“…emptiness test is based on the Kleene's system of "strong connectives" (Panti, 1995). (The special definition of implications of this system is not required in the presented approach.)…”

Section: Emptiness Test Of Annotated Fsamentioning

confidence: 99%

Matchmaking for Business Processes Based on Choreographics

Wombacher¹,

Fankhauser²,

Mahleko³

et al. 2004

International Journal of Web Services Research

View full text Add to dashboard Cite

Web services have a potential to enhance B2B e-commerce over the Internet by allowing companies and organizations to publish their business processes on service directories where potential trading partners can find them. This can give rise to new business paradigms based on ad-hoc trading relations as companies, particularly small to medium scale, can cheaply and flexibly enter into fruitful contracts, for example through subcontracting from big companies by simply publishing their business processes and the services they offer. More business process support by the Web service infrastructure is however needed before such a paradigm change can materialize. A service for searching and matchmaking of business processes does not yet exist in the current infrastructure. We believe that such a service is needed and will enable companies and organizations to be able to establish ad-hoc business relations without relying on manually negotiated interorganizational workflows. This article gives a formal semantics to business process matchmaking based on finite state automata extended by logical expressions associated to states.

show abstract

Multi-Valued Logics

Cited by 13 publications

References 70 publications

Analytic Continuation of $ζ(s)$ Violates the Law of Non-Contradiction (LNC)

Analytic Continuation of $ζ(s)$ Violates the Law of Non-Contradiction (LNC)

Matchmaking for business processes based on choreographies

Matchmaking for Business Processes Based on Choreographics

Contact Info

Product

Resources

About