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On Quantified Modal Theorem Proving for Modeling Ethics

Naveen Sundar Govindarajulu, Selmer Bringsjord, Matthew Peveler
2019 Electronic Proceedings in Theoretical Computer Science  
Logics for modeling ethical theories, and their automated reasoners, have requirements that are different from modal logics used for other purposes, e.g. for temporal reasoning.  ...  Particularly, a quantified modal logic, the deontic cognitive event calculus (DCEC), has been used to model various versions of the doctrine of double effect, akrasia, and virtue ethics.  ...  These ethical principles and theories have a unique set of characteristics when compared with other domains, e.g. with temporal reasoning, in which modal logics have been used. 1 This implies that logics  ... 
doi:10.4204/eptcs.311.7 fatcat:wew5qwpw3nar7hcawq2j522e4e

Page 9531 of Mathematical Reviews Vol. , Issue 2004m [page]

2004 Mathematical Reviews  
The final part of the paper outlines the approach used to obtain the results and the automated reasoning strategies used.  ...  All the proofs reported were discovered with the assistance of the automated reasoning program Otter.  ... 

On Temporal and Separation Logics (Invited Paper)

Stéphane Demri, Michael Wagner
2018 International Symposium/Workshop on Temporal Representation and Reasoning  
In this talk, we illustrate how several features of separation logics, for instance the key concept of separation, are related to similar notions in temporal logics.  ...  This is also the opportunity to present bridges between well-known temporal logics and more recent separation logics.  ...  logics, see e.g. [5, 33, 18] , in order to reason about resources in a temporal framework.  ... 
doi:10.4230/lipics.time.2018.1 dblp:conf/time/Demri18 fatcat:hltoioogqjdoxmd5lyfgy5kwna

Page 5554 of Mathematical Reviews Vol. , Issue 94j [page]

1994 Mathematical Reviews  
(NL-DELF-CS; Delft) Generic resolution in propositional modal systems. (English summary) Logic programming and automated reasoning (St. Petersburg, 1993), 241-252, Lecture Notes in Comput.  ...  (English summary) Logic programming and automated reasoning (St. Petersburg, 1993), 253-264, Lecture Notes in Comput. Sci., 698, Springer, Berlin, 1993.  ... 

Applications of scott's notion of consequence to the study of general binary intensional connectives and entailment

Dov M. Gabbay
1973 Journal of Philosophical Logic  
Reidel, 1976. 321 pp, The main research thrust of this monograph is to present comprehensive methods for proving decidability and undecidability for modal and temporal systems.  ...  This paper is the first in a series in reformulating classical and non-classical logic in a goal directed way.  ...  Modal and Temporal Logic Programming In Temporal Logics and Their Applications, A. Galton, ed. pp 197-237. Academic Press, 1987 .  ... 
doi:10.1007/bf00129607 fatcat:e6lokulrwrfcvl525fgj6dcr3m

Saturation-based theorem proving: Past successes and future potential [chapter]

Harald Ganzinger
1996 Lecture Notes in Computer Science  
calculi for modal and temporal logics p. 598 Tableaux and algorithms for propositional dynamic logic with converse p. 613 Reflection of formal tactics in a deductive reflection framework p. 628  ...  Proof search with set variable instantiation in the calculus of constructions p. 658Search strategies for resolution in temporal logics p. 673Optimal axiomatizations for multiple-valued operators and quantifiers  ... 
doi:10.1007/3-540-61511-3_64 fatcat:iizfu32trnfadmj4z7xcvwds5y

Higher-order aspects and context in SUMO

Christoph Benzmüller, Adam Pease
2012 Journal of Web Semantics  
This way automated higher-order theorem provers can be safely applied for reasoning about modal contexts in SUMO.  ...  A solution is proposed that maps SUMO to quantified multimodal logic which is in turn modeled as a fragment of classical higher-order logic.  ...  We would like to thank Geoff Sutcliffe and Larry Paulson for their support and their contributions to our work. Moreover, we thank the reviewers of this article for many fruitful comments.  ... 
doi:10.1016/j.websem.2011.11.008 fatcat:vml7qpbtg5fwziok2ehvgw6ynq

Automating Quantified Multimodal Logics in Simple Type Theory -- A Case Study [article]

Christoph Benzmueller
2009 arXiv   pre-print
In a case study we investigate whether off the shelf higher-order theorem provers and model generators can be employed to automate reasoning in and about quantified multimodal logics.  ...  In our experiments we exploit the new TPTP infrastructure for classical higher-order logic.  ...  quantified temporal logics.  ... 
arXiv:0905.4369v1 fatcat:bcudk2sfdbfq3buikviucbzedu

Page 5446 of Mathematical Reviews Vol. , Issue 2002H [page]

2002 Mathematical Reviews  
tableaux for variants of quantified modal logics.  ...  “This paper is an extended version of a previous work by the authors [in Automated reasoning with analytic tableaux and related methods (St. Andrews, 2000), 175-189, Lecture Notes in Comput.  ... 

Interacting with Modal Logics in the Coq Proof Assistant [chapter]

Christoph Benzmüller, Bruno Woltzenlogel Paleo
2015 Lecture Notes in Computer Science  
This paper describes an embedding of higher-order modal logics in the Coq proof assistant.  ...  Coq's capabilities are used to implement modal logics in a minimalistic manner, which is nevertheless su cient for the formalization of significant, non-trivial modal logic proofs.  ...  We thank Cedric Auger and Laurent Théry, for their answers to our questions about Ltac in the Coq-Club mailing-list.  ... 
doi:10.1007/978-3-319-20297-6_25 fatcat:meeyvyre7zh3rb3wy6rjknyf6y

Page 6407 of Mathematical Reviews Vol. , Issue 95k [page]

1995 Mathematical Reviews  
Maslov’s result [in Automation of reasoning. 2, 264-272, Springer, Berlin, 1983; see MR 84f:03011b] on the connection between the resolution method and the inverse method for the classical predicate calculus  ...  In the current paper he extends it for the quantified modal systems S4, T, K4, K, and SS. The paper begins with the formulation of N. K. Zamov’s [Ann. Pure Appl.  ... 

Page 5092 of Mathematical Reviews Vol. , Issue 95i [page]

1995 Mathematical Reviews  
useful device in the process of automated translation between modal logics and classical logic.  ...  Mironov (RS-MOSC-SL; Moscow) 95i:03043 03B45 03B35 68T15 68T27 Szalas, Andrzej (PL-WASW-I; Warsaw) On an automated translation of modal proof rules into formulas of the classical logic.  ... 

Page 409 of Mathematical Reviews Vol. , Issue 93a [page]

1993 Mathematical Reviews  
The authors give a modal temporal logic based on time intervals. The paper provides motivations from fields of AI for building such a logic.  ...  Vari- able (quantifier) elimination is the key underlying operation which provides an oracle to answer all queries and plays a role simi- lar to resolution in logic programming.  ... 

Combining and automating classical and non-classical logics in classical higher-order logics

Christoph Benzmüller
2011 Annals of Mathematics and Artificial Intelligence  
In this article we focus on combinations of (quantified) epistemic and doxastic logics and study their application for modeling and automating the reasoning of rational agents.  ...  Examples include propositional and quantified multimodal logics, intuitionistic logics, logics for security, and logics for spatial reasoning.  ...  Geoff Sutcliffe, in collaboration with the author and supported by several further contributors, developed the new higher-order TPTP THF infrastructure (EU FP7 grant THFTPTP PIIF-GA-2008-219982).  ... 
doi:10.1007/s10472-011-9249-7 fatcat:4ppv6v36njcshd327mvguuj52a

Forthcoming papers

1997 Artificial Intelligence  
Many themes in nonmonotonic reasoning concern implicit and explicit definability. implicit definability in nonmonotonic logic is always relative to the context-the current theory of the world.  ...  Kuipers, Proving properties of continuous systems: qualitative simulation and temporal logic We demonstrate an automated method for proving temporal logic statements about solutions to ordinary differential  ...  Kuipers, Proving properties of continuous systems: qualitative simulation and temporal logic We demonstrate an automated method for proving temporal logic statements about solutions to ordinary differential  ... 
doi:10.1016/s0004-3702(97)90013-8 fatcat:go56fm6hmvap7dcxp5nnvy4xxq
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