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BOOK REVIEW: CARNIELLI, W., CONIGLIO, M. Paraconsistent Logic: Consistency, Contradiction and Negation. Logic, Epistemology, and the Unity of Science Series. (New York: Springer, 2016. ISSN: 2214-9775.)

Henrique Antunes, Vincenzo Ciccarelli
2018 Manuscrito  
Review of the book 'Paraconsistent Logic: Consistency, Contradiction and Negation' (2016), by Walter Carnielli and Marcelo Coniglio  ...  employed in the definition of substitutional semantics for first-order logic.  ...  Due to the nondeterministic nature of mbC, a non-standard semantics is defined for its first-order extension: the authors introduce the notion of a Tarskian paraconsistent structure, defined as an ordered  ... 
doi:10.1590/0100-6045.2018.v41n2.hv fatcat:x5s4w3idb5eftoxmye2ydks62e

Page 5451 of Mathematical Reviews Vol. , Issue 2002H [page]

2002 Mathematical Reviews  
.], where this concept was referred to as ‘non-deterministic semantics’). “Here we try to clarify this new concept, reformulating the ideas of [W. A.  ...  First, we point out that, among non-classical logics, finite multi-valued logics possess semantic interpretations which are both intuitively acceptable and easy to manipulate formally.  ... 

Non-deterministic Multi-valued Logics--A Tutorial

Arnon Avron, Anna Zamansky
2010 2010 40th IEEE International Symposium on Multiple-Valued Logic  
In this tutorial we introduce the reader to the concept of Nmatrices, and demonstrate their usefulness by providing modular non-deterministic semantics for a well-known family of logics for reasoning under  ...  Non-deterministic multi-valued matrices (Nmatrices) are a new, fruitful and quickly expanding field of research first introduced a few years ago.  ...  We will now provide modular non-deterministic semantics for a selection of LFIs considered in the literature. We start with the basic paraconsistent logic over Ä AE .  ... 
doi:10.1109/ismvl.2010.18 dblp:conf/ismvl/AvronZ10 fatcat:ccoeqnhvfvbrvheu3cvcmpf47y

Defining LFIs and LFUs in extensions of infectious logics

Damian Enrique Szmuc
2016 Journal of Applied Non-Classical Logics  
The aim of this paper is to explore the peculiar case of infectious logics, a group of systems obtained generalizing the semantic behavior characteristic of the {¬, ∧, ∨}-fragment of the logics of nonsense  ...  Here, we extend these logics with classical negations, and we furthermore show that some of these extended systems can be properly regarded as Logics of Formal Inconsistency (LFIs) and Logics of Formal  ...  Acknowledgements I am grateful to Eduardo Barrio, Federico Pailos, Lucas Rosenblatt and all the members of BA-LOGIC (Buenos Aires Logic Group) for their comments on earlier versions of this paper.  ... 
doi:10.1080/11663081.2017.1290488 fatcat:czle7u7gxrbili5z42fmvkqzyu

Compositional Meaning in Logic

Carlos Caleiro, Luca Viganò
2017 Logica Universalis  
Within the domain of formal semantics and of the structure of logical derivations, the PoC is often directly reflected by metaproperties such as truth-functionality and analyticity, characteristic of computationally  ...  well-behaved logical systems.  ...  In particular, one of the main methods for developing Gentzen-type systems for non-classical logics is precisely to translate many-valued semantics (deterministic or non-deterministic) into a bivalent  ... 
doi:10.1007/s11787-017-0177-0 fatcat:wtzoqtae6jahpcmrbt2hscswam

Non-deterministic Multi-valued Matrices for First-Order Logics of Formal Inconsistency

Arnon Avron, Anna Zamansky
2007 Proceedings - International Symposium on Multiple-Value Logic  
Paraconsistent logic is the study of contradictory yet non-trivial theories.  ...  In this paper we use nondeterministic matrices, a generalization of standard multivalued matrices, to provide simple and modular finitevalued semantics for a large family of first-order LFIs.  ...  ., a n ] ⊆ M 1 [ Non-deterministic semantics for LFIs In this section we provide non-deterministic semantics for the first-order LFIs obtained from the basic system QB by adding various combinations  ... 
doi:10.1109/ismvl.2007.38 dblp:conf/ismvl/AvronZ07 fatcat:7djzcygf2fhwnpcd4we2tsrzmi

Tools for the Investigation of Substructural and Paraconsistent Logics [chapter]

Agata Ciabattoni, Lara Spendier
2014 Lecture Notes in Computer Science  
This system introduces analytic calculi for large classes of substructural and paraconsistent logics, which it then uses to prove various results about the formalized logics.  ...  complete (and hence it is a fuzzy logic in the sense of [20, 17] ) and (ii) to extract non-deterministic finite-valued semantics for paraconsistent and related logics and provide a uniform decidability  ...  An Application: Non-deterministic Semantics The introduced calculi, obtained by extending LK + with the special rules described in Theorem 2, are used to extract new semantics for the corresponding logics  ... 
doi:10.1007/978-3-319-11558-0_2 fatcat:ez3itzximrgwxlilpuci5gkgky

BOOK REVIEW: CARNIELLI, Walter & MALINOWSKI, Jacek (eds.). Contradictions, from Consistency to Inconsistency (Trends in Logic 47, Springer International Publishing, 2018, VI+322 pages)

RAFAEL R. TESTA
2019 Manuscrito  
Most of them are developed around a fine-grained investigation on the principle of non-contradiction and the concept of consistency, inquired mainly into the broad area of paraconsistent logics.  ...  The book itself is the result of a work that was initiated on the Studia Logica conference "Trends in Logic XVI: Consistency, Contradiction, Paraconsistency and Reasoning -40 years of CLE", held at the  ...  The techniques used allow for a modular analysis of the logics, providing complete semantics based on (non-deterministic) logical matrices and complexity upper bounds.  ... 
doi:10.1590/0100-6045.2019.v42n1.rt fatcat:fq4htyfyc5bhtdsjqhiqfxzvqe

Ordered pair semantics and negation in LP

Matthew Clemens
2020 The Australasian Journal of Logic  
In this note, I present a modified semantic framework for the multi-valued paraconsistent logic LP, which allows for a straightforward preservation of a significant classical intuition about negation,  ...  e.g., Wansing 1993 and Pynko 1995 , and with the non-deterministic semantics developed in work of Avron (see Avron and Zamansky 2011 for an overview).  ...  Hardegree Symbolic Logic: A First Course online (using the term 'opposite'). 2 'LP' is the now standard name for the paraconsistent logic developed as early as 1966 (Asenjo 1966), and independently in  ... 
doi:10.26686/ajl.v17i5.4080 fatcat:764qe6rds5dthjesa6uftlzroq

Modular Construction of Cut-free Sequent Calculi for Paraconsistent Logics

Arnon Avron, Beata Konikowska, Anna Zamansky
2012 2012 27th Annual IEEE Symposium on Logic in Computer Science  
The method relies on the use of nondeterministic semantics for these logics.  ...  This paper makes a substantial step towards automatization of paraconsistent reasoning by providing a general method for a systematic and modular generation of cut-free calculi for thousands of paraconsistent  ...  Non-deterministic Three-valued Semantics Our non-deterministic semantics is based on the following four truth-values, the intuition being that a formula ϕ is assigned a truth-value of the form x, y , where  ... 
doi:10.1109/lics.2012.20 dblp:conf/lics/AvronKZ12 fatcat:siegiuf2tfepteyqjifwqrcrme

A Note on Ciuciura's mbC1

Hitoshi Omori
2019 Bulletin of the Section of Logic  
This note offers a non-deterministic semantics for mbC1, introduced by Janusz Ciuciura, and establishes soundness and (strong) completeness results with respect to the Hilbert-style proof system.  ...  Moreover, based on the new semantics, we briefly discuss an unexplored variant of mbC1 which has a contra-classical flavor.  ...  A revised version was prepared during my visit to UNAM which was made possible by the grant PAPIIT project IA401117 "Philosophical Aspects of Contra-Classical Logics".  ... 
doi:10.18778/0138-0680.48.3.01 fatcat:3r3zk4e2jrdqvk2ba3dsg22shm

Non-deterministic Semantics in Polynomial Format

Walter Carnielli, Mariana Matulovic
2014 Electronical Notes in Theoretical Computer Science  
Although useful in general domains, as in first-order logic, certain non-truth-functional logics and even in modal logics (see [1] ), the method is particularly apt for deterministic and non-deterministic  ...  of a software capable of translating provability in deterministic and non-deterministic finite-valued logical systems into operations on polynomial rings.  ...  Acknowledgement This research was financed by FAPESP (Thematic Project LogCons 2010/51038-0, Brazil) and by individual research grants from The National Council for Scientific and Technological Development  ... 
doi:10.1016/j.entcs.2014.06.003 fatcat:kmmemfe26nacrb227r4rr3e5f4

Paraconsistency and its Philosophical Interpretations

Eduardo Barrio, Bruno Da Re
2018 The Australasian Journal of Logic  
In this paper, we argue against this connection and show that it is perfectly possible to adopt a paraconsistent logic and reject dialetheism, and, moreover, that there are examples of non-paraconsistent  ...  However, paraconsistency is a formal feature of some logics that consists in invalidating the rule of explosion, whereas dialetheism is a semantical/ontological position consisting in accepting true contradictions  ...  Acknowledgments We would like to thank the members of the Buenos Aires Logic Group for helpful feedback concerning previous versions of this paper.  ... 
doi:10.26686/ajl.v15i2.4860 fatcat:vkhma5klzjb3pa4uhfsghe2r3i

Many-Valued Non-deterministic Semantics for First-Order Logics of Formal (In)consistency [chapter]

Arnon Avron, Anna Zamansky
2007 Lecture Notes in Computer Science  
In this paper we provide non-deterministic semantics for a very large family of first-order LFIs (which includes da Costa's original system C * 1 , as well as thousands of other logics).  ...  first-order paraconsistent system.  ...  Non-deterministic semantics for first-order LFIs Finite non-deterministic semantics In this section we provide five-valued (or less) non-deterministic semantics for first-order LFIs obtained from the  ... 
doi:10.1007/978-3-540-75939-3_1 fatcat:um6iomipy5bdhii5cpk6w7xltq

Cut-free sequent calculi for C-systems with generalized finite-valued semantics

A. Avron, B. Konikowska, A. Zamansky
2012 Journal of Logic and Computation  
In [5], a general method was developed for generating cut-free ordinary sequent calculi for logics that can be characterized by finite-valued semantics based on non-deterministic matrices (Nmatrices).  ...  In this paper, a substantial step towards automation of paraconsistent reasoning is made by applying that method to a certain crucial family of thousands of paraconsistent logics, all belonging to the  ...  However, [12] provided finite non-deterministic semantics for first-order C-systems, which could be exploited along the lines of the approach presented here. • As we have noted in Remark 38, all the  ... 
doi:10.1093/logcom/exs039 fatcat:pjdwo2adfzeu7eqexvoshj7ap4
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