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Page 5452 of Mathematical Reviews Vol. , Issue 2002H [page]

2002 Mathematical Reviews  
“We introduce the algebras of these logics, as the logic trans- formers we consider have simple characterizations in terms of these algebras.  ...  In this paper I present probabilistic semantics for the paraconsistent logics of first degree entailment (FDE) and the logic of paradox (LP). The paper is in four sections.  ... 

The role of logical interpretations in program development

Manuel Martins, Alexandre Madeira, Luis Barbosa, Andrzej Tarlecki
2014 Logical Methods in Computer Science  
Stepwise refinement of algebraic specifications is a well known formal methodology for program development.  ...  However, traditional notions of refinement based on signature morphisms are often too rigid to capture a number of relevant transformations in the context of software design, reuse, and adaptation.  ...  Acknowledgements The authors express their gratitude to the anonymous referees who raised a number of pertinent questions entailing a more precise characterisation of the paper's contributions and a clarification  ... 
doi:10.2168/lmcs-10(1:1)2014 fatcat:g6p3ishlk5be5au3aj2tmdxv5e

Refinement by Interpretation in a General Setting

Manuel A. Martins, Alexandre Madeira, Luis S. Barbosa
2009 Electronical Notes in Theoretical Computer Science  
This paper goes a step forward and discusses the generalization of this idea to deductive systems of arbitrary dimension.  ...  Refinement by interpretation replaces signature morphisms by logic interpretations as a means to translate specifications and witness refinements.  ...  Towards algebraic semantics There are k-logics to which an algebraic specification can be associated, thus providing an alternative semantics (called algebraic semantics in the context of algebraic logic  ... 
doi:10.1016/j.entcs.2009.12.020 fatcat:mp4brly7q5e6jogzs4qeycnxdy

On a New Idiom in the Study of Entailment

R. E. Jennings, Y. Chen, J. Sahasrabudhe
2011 Logica Universalis  
of the entailed sentence is underwritten by an atomic constituent of the entailing one.  ...  Since the lattice of hypergraphs thus ordered is a DeMorgan lattice, the logic of entailment thus understood is the familiar system, FDE of first-degree entailment.  ...  Introducing analytic semantics A traditional principle of entailment asserts that for α to entail β, β must be 'contained' in α. The notion of 'containment' can be interpreted in various ways.  ... 
doi:10.1007/s11787-011-0027-4 fatcat:axevkluf2rakdjbvlyfnisxexu

Behavioral equivalence of hidden k -logics: An abstract algebraic approach

Sergey Babenyshev, Manuel A. Martins
2016 Journal of Applied Logic  
It uses a generalization of the notion of an abstract deductive system to handle multi-sorted deductive systems which differentiate visible and hidden sorts.  ...  This work advances a research agenda which has as its main aim the application of Abstract Algebraic Logic (AAL) methods and tools to the specification and verification of software systems.  ...  The second author also acknowledges the financial assistance by EU FP7 Marie Curie PIRSES-GA-2012-318986 project GeTFun and the project FFI2013-47126-P by the Spanish Ministry of Research.  ... 
doi:10.1016/j.jal.2016.03.002 fatcat:lsbvjqsey5bdbalrlkgui4k7la

Page 519 of Mathematical Reviews Vol. , Issue 2002A [page]

2002 Mathematical Reviews  
The authors consider an algebraic specification language that, be- sides concurrency, synchronization and nondeterminism, encom- passes the notion of time.  ...  “To equip transitions (actually, rewriting steps) with an algebraic structure is also a key point of the rewriting logic approach: a system is considered as a logical theory, and any sequence of transitions  ... 

Page 37 of Mathematical Reviews Vol. , Issue 2001A [page]

2001 Mathematical Reviews  
A comparison of the semantic- logic-theoretic and set-measure-theoretic approaches presented is given. Finally, the notion of logical consequences of statements about probability is introduced.  ...  After presenting the motivations (Sec- tion 1) and giving an introduction to structures of truth degrees (Section 2), the notion of a system with many-valued information is presented (Section 3) such a  ... 

Probabilistic ABox Reasoning: Preliminary Results

Michael Dürig, Thomas Studer
2005 International Workshop on Description Logics  
Most probabilistic extensions of description logics focus on the terminological apparatus.  ...  We introduce syntax and semantics for PALC and we define the corresponding reasoning problem.  ...  First, we define the notion of j-consistency which will be the dual of the entailment relation.  ... 
dblp:conf/dlog/DurigS05 fatcat:5vgvccuw35gavengligt2rkruy

Hierarchical logical consequence

C. Caleiro, P. Gouveia, J. Ramos
2010 Logic Journal of the IGPL  
The modern view of logical reasoning as modeled by a consequence operator (instead of simply by a set of theorems) has allowed for huge developments in the study of logic as an abstract discipline.  ...  In order to illustrate the usefulness of the notion of hierarchical consequence operators we address a few questions in the theory of combined logics, where a suitable abstract presentation of the logics  ...  To this end, we consider semantic systems based on the notion of satisfaction.  ... 
doi:10.1093/jigpal/jzp093 fatcat:s6q57ex36vft5hnxrakpqwc3ty

The semantic foundations of concurrent constraint programming

Vijay A. Saraswat, Martin Rinard, Prakash Panangaden
1991 Proceedings of the 18th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '91  
Indeed, the origins of the cc framework are in concurrent logic programming and in the notion of constraint logic programing intro. duced by [JL87,Mah8~. See [Sar89] for further details.  ...  Concurrent constraint programming [Sar89 ,SR90] is a simple and powerful model of concurrent computation based on the notions of store-as-constraint and process as information straint programming framework  ...  @ 1990 ACM 089791-419-8/90/0012/0333 $1.50 a simple operational semantics (which dispenses with the explicit notions of renaming that plague logic programming semantics), and show  ... 
doi:10.1145/99583.99627 dblp:conf/popl/SaraswatRP91 fatcat:2t2lyephjjfkdfwfoj23z646fq

Satisfiability Calculus: The Semantic Counterpart of a Proof Calculus in General Logics [chapter]

Carlos Gustavo López Pombo, Pablo F. Castro, Nazareno M. Aguirre, Thomas S. E. Maibaum
2013 Lecture Notes in Computer Science  
an entailment system together with an institution, see Def. 6.  ...  In this paper we intend to complete this picture by providing the notion of Satisfiability Calculus, which might be thought of as the semantical counterpart of the notion of proof calculus, that provides  ...  As introduced by Meseguer, the notion of proof calculus provides, intuitively, an implementation of the entailment relation of a logic.  ... 
doi:10.1007/978-3-642-37635-1_12 fatcat:c367lec4pbglzlf7dji2o6edyq

Congruence Filter Pairs, Adjoints and Leibniz Hierarchy [article]

Peter Arndt, Hugo Luiz Mariano, Darllan Conceição Pinto
2021 arXiv   pre-print
We show that the class of logics admitting a presentation by such a filter pair is exactly the class of logics having an algebraic semantics.  ...  We review the notion of (finitary) filter pair as a tool for creating and analyzing logics.  ...  This comes from the possibility of giving an algebraic semantics to an algebraizable logic that is not an equivalent algebraic semantics.  ... 
arXiv:2109.01065v1 fatcat:3cxmtcpnebgpnmzo77wbila5oe

Clausal Logic and Logic Programming in Algebraic Domains

William C Rounds, Guo-Qiang Zhang
2001 Information and Computation  
Chains and directed sets provide us with an abstract notion of \approximatingsequence", where \approximation" is in the sense of learning more and more speci c information.  ...  their equivalence; nally, we apply our results to give both a syntax and semantics for default logic in any coherent algebraic dcpo.  ...  We are going to tie this notion of an extension to the semantic version of extensions found in ZR97a] and in RZ97].  ... 
doi:10.1006/inco.2001.3073 fatcat:k6gdk63x5remze6bguktcpqtty

Logical Grammar [chapter]

Glyn Morrill
2012 Philosophy of Linguistics  
Sequent calculus First-order entailment is an infinitary semantic notion since it appeals to the class of all interpretations.  ...  Proof theory aims to capture such semantic notions as entailment in finitary syntactic formal systems.  ... 
doi:10.1016/b978-0-444-51747-0.50003-2 fatcat:ywfi5re5brem7f4mvyaiyrq7t4

Does information inform confirmation?

Colin Howson
2015 Synthese  
defective measure of information, while the other, although an admissible measure of information, generates a defective measure of confirmation.  ...  I argue that of the two explicata of semantic information (due originally to Bar Hillel and Carnap) which are considered by the authors, the one generating a popular Bayesian confirmation measure is a  ...  There is no paradox, and certainly no inconsistency, in this proposal: the Cn(a) might not form an algebra, but the set of all subsets of the set of sentences of whatever language L is involved is an algebra  ... 
doi:10.1007/s11229-015-0918-7 fatcat:yitgjzf6kjho5mhdmy2xk6wt5u
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