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A Paraconsistent Higher Order Logic [article]

Jørgen Villadsen
2003 arXiv   pre-print
We present a concise description of a paraconsistent higher order logic with countable infinite indeterminacy, where each basic formula can get its own indeterminate truth value (or as we prefer: truth  ...  A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to achieve there are many potential applications of paraconsistent  ...  We present a paraconsistent higher order logic ∇ based on the (simply) typed λ-calculus [18, 4] .  ... 
arXiv:cs/0207088v3 fatcat:4rjzpyc6qjdntkxici5zb3dohq

A Paraconsistent Higher Order Logic [chapter]

Jørgen Villadsen
2004 Lecture Notes in Computer Science  
We present a concise description of a paraconsistent higher order logic with countable infinite indeterminacy, where each basic formula can get its own indeterminate truth value (or as we prefer: truth  ...  A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to achieve there are many potential applications of paraconsistent  ...  We present a paraconsistent higher order logic ∇ based on the (simply) typed λ-calculus [18, 4] .  ... 
doi:10.1007/978-3-540-30210-0_5 fatcat:kexdmfwtw5avjotims7kmr3ive

Page 2318 of Mathematical Reviews Vol. , Issue 2002D [page]

2002 Mathematical Reviews  
ISBN 0-19-726182-5 Contents: James Higginbotham, On higher-order logic and natural language (1-27); David Bostock, On motivating higher-order logic.  ...  Kirchner, Combining higher-order and first-order compu- tation using p-calculus: towards a semantics of ELAN (95-119); Chiara Ghidini and Luciano Serafini, Distributed first order log- ics (121-139);  ... 

Page 6607 of Mathematical Reviews Vol. , Issue 92m [page]

1992 Mathematical Reviews  
Some modal and discussive systems, generalized Jaskowski logics, higher-order discussive logic and set theory are then studied by J. Kotas and da Costa. R. K. Meyer and J. K.  ...  In order to discuss the present-day development of paraconsistent logic, the author analyses the main systems and results by outlining this development country by country.  ... 

Paraconsistent Assertions [chapter]

Jørgen Villadsen
2004 Lecture Notes in Computer Science  
We argue that paraconsistent logics are especially advantageous in order to deal with assertions made by intelligent agents.  ...  We propose a many-valued paraconsistent logic based on a simple notion of indeterminacy.  ...  We recently developed a so-called sequent calculus for a higher order logic extension of the paraconsistent logic ∇ [28] .  ... 
doi:10.1007/978-3-540-30082-3_8 fatcat:jscwklwnlvcrndfziznnmij2o4

Learning Evaluation Using Non-classical Logics [chapter]

Genivaldo Carlos Silva, Jair Minoro Abe
2015 IFIP Advances in Information and Communication Technology  
The Paraconsistent Annotated Evidential Eτ Logic proves to be helpful in the analysis of these data types in order to see more clearly the items that should be improved.  ...  This work presents a case study using a non-classical logic, to analyze these conflicting views.  ...  first-order predicate calculi (with and without equality), of paraconsistent description calculi, and paraconsistent higher-order logics (systems NF i ,1 ≤ i ≤ ω).  ... 
doi:10.1007/978-3-319-22756-6_68 fatcat:aahsrqxhbzhq5m6g42bxzcy3tq

Page 2729 of Mathematical Reviews Vol. , Issue 2004d [page]

2004 Mathematical Reviews  
This sys- tem was later extended to lower and higher order predicate calculus [N. C. A. da Costa, Rep. Math. Logic No. 4 (1975), 7-15; MR 52 03B General logic 20044:03060 #2821; N.C.  ...  Summary: “A survey is given of three-valued paraconsistent propo- sitional logics connected with JaSkowski’s criterion for constructing paraconsistent logics.  ... 

Page 8876 of Mathematical Reviews Vol. , Issue 2000m [page]

2000 Mathematical Reviews  
Summary: “We set up a framework for the study of extensional- ity in the context of higher-order logic programming.  ...  Some typical examples of higher-order logic programs are shown to be extensional.”  ... 

Meeting Hintikka's Challenge to Paraconsistentism

Walter Carnielli
2009 Principia: An International Journal of Epistemology  
One of the major difficulties, left as a challenge, would be to formulate some truth conditions for this new paraconsistent first-order language in order to make IF logic and paraconsistent logic more  ...  Jaakko Hintikka, in a series of talks in Brazil in 2008, defended that IF ("independence-friendly") logic and paraconsistent logic are, in a sense, very similar.  ...  Expressing other concepts like infinity and equicardinality, which need higher-order logics, is also possible in IF logic.  ... 
doi:10.5007/1808-1711.2009v13n3p283 fatcat:xiflhetswzeblesa6pbvjiidxq

Paraconsistent Semantics for Hybrid MKNF Knowledge Bases [chapter]

Shasha Huang, Qingguo Li, Pascal Hitzler
2011 Lecture Notes in Computer Science  
In this paper, we employ the four-valued logic proposed by Belnap, and present a paraconsistent semantics for Hybrid MKNF knowledge bases, which can detect inconsistencies and handle it effectively.  ...  Moreover, we provide a fixpoint algorithm for computing paraconsistent MKNF models.  ...  Definition 6 A four-valued (paraconsistent) MKNF structure (I, M, N ) consists of a paraconsistent Herbrand first-order interpretation I and two nonempty sets of paraconsistent Herbrand first-order interpretations  ... 
doi:10.1007/978-3-642-23580-1_8 fatcat:k7o5l6j56rblzlphvvtjhxwhd4

New Formalized Results on the Meta-Theory of a Paraconsistent Logic

Anders Schlichtkrull, Michael Wagner
2019 Types for Proofs and Programs  
Classical logics are explosive, meaning that everything follows from a contradiction. Paraconsistent logics are logics that are not explosive.  ...  This paper presents the meta-theory of a paraconsistent infinite-valued logic, in particular new results showing that while the question of validity for a given formula can be reduced to a consideration  ...  The same specification could be used for giving a semantics to the paraconsistent higher-order logic.  ... 
doi:10.4230/lipics.types.2018.5 dblp:conf/types/Schlichtkrull18 fatcat:tlaj367ukbdtvewxseimupemmq

Supra-logic: using transfinite type theory with type variables for paraconsistency

Jørgen Villadsen
2005 Journal of Applied Non-Classical Logics  
We define the paraconsistent supra-logic Pσ by a type-shift from the booleans o of propositional logic Po to the supra-booleans σ of the propositional type logic P obtained as the propositional fragment  ...  of the transfinite type theory Q defined by Peter Andrews (North-Holland Studies in Logic 1965) as a classical foundation of mathematics.  ...  Non-classical higher order logics are possible, e.g. intuitionistic higher order logic [24] .  ... 
doi:10.3166/jancl.15.45-58 fatcat:drzazf2wxjhi3cpvo7u7saprbe

An Expert System Structured in Paraconsistent Annotated Logic for Analysis and Monitoring of the Level of Sea Water Pollutants [chapter]

Joao Inacio Da Silva Filho, Mauricio C., Camilo D. Seabra Pereira, Ana Carolina, Luis Fernando P. Ferrara, Odair Pitoli, Dorotea Vilanova
2011 Expert Systems for Human, Materials and Automation  
The learning Factor l F is a real value, equal or higher than 0, got arbitrarily through external adjustments. The higher the value of l F higher is the learning process of the cell.  ...  Paraconsistent Annotated Logics The Paraconsistent Annotated Logics are classes of Paraconsistent Logics that have a lattice associate and were introduced for the first time in programming logic by Subrahmanian  ...  An Expert System Structured in Paraconsistent Annotated Logic for Analysis and Monitoring of the Level of Sea Water Pollutants, Expert Systems for Human, Materials and Automation, Prof.  ... 
doi:10.5772/17603 fatcat:gqtloujx2vcddfak3gzrg52mrq

Reasoning with inconsistencies in hybrid MKNF knowledge bases

S. Huang, Q. Li, P. Hitzler
2012 Logic Journal of the IGPL  
More precisely, we present a paraconsistent semantics for hybrid MKNF knowledge bases (called para-MKNF knowledge bases) based on four-valued logic as proposed by Belnap.  ...  in our paradigm is not higher than that of classical reasoning.  ...  It is a variant of first-order modal logic with two modal operators: K and not.  ... 
doi:10.1093/jigpal/jzs043 fatcat:2i7ix42byvdr3lztmwc6shxwxa

Priority Modes of Transport for Soybeans from the Center-West Region in Brazil [chapter]

Cristina Corrêa de Oliveira, Danilo Medeiros de Castro, Nélio Fernando dos Reis, João Gilberto Mendes dos Reis, Jair Minoro Abe
2015 IFIP Advances in Information and Communication Technology  
This article intends to explain the use of the Paraconsistent Decision Method based on the Evidential Annotated Paraconsistent Logic Eτ in the decision-making process involving experts in priority modes  ...  first-order predicate calculi (with and without equality), of paraconsistent description calculi, and paraconsistent higher-order logics (systems NF i , 1 ≤ i ≤ ω).  ...  A paraconsistent logic is a logic that can be used as the basis for inconsistent but non-trivial theories. A theory is called paraconsistent if its underlying logic is a paraconsistent logic.  ... 
doi:10.1007/978-3-319-22756-6_40 fatcat:yxtxragj3rga5d2mqf3eftx6ji
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