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Cut-Elimination for Quantified Conditional Logic

Christoph Benzmüller
2016 Journal of Philosophical Logic  
A semantic embedding of quantified conditional logic in classical higher-order logic is utilized for reducing cut-elimination in the former logic to existing results for the latter logic.  ...  The presented embedding approach is adaptable to a wide range of other logics, for many of which cut-elimination is still open.  ...  In this article the embedding approach is exemplarily utilized for proving cut-elimination for quantified conditional logics (QCL).  ... 
doi:10.1007/s10992-016-9403-0 fatcat:q7zx3yrfejfnfjkkhwa2mav3ba

Universal (meta-)logical reasoning: Recent successes

Christoph Benzmüller
2019 Science of Computer Programming  
Classical higher-order logic, when utilized as a meta-logic in which various other (classical and non-classical) logics can be shallowly embedded, is suitable as a foundation for the development of a universal  ...  A respective universal logical reasoning framework is described in this article and a range of successful first applications in philosophy, artificial intelligence and mathematics are surveyed.  ...  While earlier, practical work in the CompMeta project had already shown that automation of quantified conditional logics is indeed feasible by utilising the SSE approach [94] , the second half of the  ... 
doi:10.1016/j.scico.2018.10.008 fatcat:xim3wn4jfbcsvl2hfdn26p6f4y

On Logic Embeddings and Gödel's God [chapter]

Christoph Benzmüller, Bruno Woltzenlogel Paleo
2015 Lecture Notes in Computer Science  
In our ongoing computerassisted study, higher-order automated reasoning tools have made some interesting observations, some of which were previously unknown.  ...  We have applied an elegant and flexible logic embedding approach to verify and automate a prominent philosophical argument: the ontological argument for the existence of God.  ...  This also includes quantified modal logics (QML) [9] and quantified conditional logics (QCL) [3] . For many of the embedded logics few or no automated theorem provers did exist before.  ... 
doi:10.1007/978-3-319-28114-8_1 fatcat:xxskykqjp5h6rbvfnzy7ylueg4

LogiKEy Workbench: Deontic Logics, Logic Combinations and Expressive Ethical and Legal Reasoning (Isabelle/HOL Dataset)

Christoph Benzmüller, Ali Farjami, David Fuenmayor, Paul Meder, Xavier Parent, Alexander Steen, Leendert van der Torre, Valeria Zahoransky
2020 Data in Brief  
More concretely, it comprises, in form of a dataset (Isabelle/HOL theory files), formal encodings of multiple deontic logics, logic combinations, deontic paradoxes and normative theories in the higher-order  ...  proof assistant system Isabelle/HOL.  ...  Supplementary Materials Supplementary material associated with this article can be found in the online version at doi: 10.1016/j.dib.2020.106409 .  ... 
doi:10.1016/j.dib.2020.106409 pmid:33134442 pmcid:PMC7586073 fatcat:rzmeu2tosvd2dn3gdz26fgtwfm

Agent-Based HOL Reasoning [chapter]

Alexander Steen, Max Wisniewski, Christoph Benzmüller
2016 Lecture Notes in Computer Science  
In the Leo-III project, a new agent-based deduction system for classical higher-order logic is developed.  ...  logics.  ...  One major goal of Leo-III is to provide native means of reasoning within (and about) non-classical logics including free logic, (quantified) conditional logic, and (quantified) modal logic 5 .  ... 
doi:10.1007/978-3-319-42432-3_10 fatcat:zh42ihlxzbgwxfj5idt7lvuin4

Designing Normative Theories for Ethical and Legal Reasoning: LogiKEy Framework, Methodology, and Tool Support [article]

Christoph Benzmüller, Xavier Parent, Leendert van der Torre
2020 arXiv   pre-print
LogiKEy's unifying formal framework is based on semantical embeddings of deontic logics, logic combinations and ethico-legal domain theories in expressive classic higher-order logic (HOL).  ...  This meta-logical approach enables the provision of powerful tool support in LogiKEy: off-the-shelf theorem provers and model finders for HOL are assisting the LogiKEy designer of ethical intelligent agents  ...  Automate: Automate the selected logics and logic combinations in HOL. In this step a selected logic or logic combination is shallowly embedded by directly encoding its semantics in meta-logic HOL.  ... 
arXiv:1903.10187v6 fatcat:f7zz3meo25ad7fcgbldwecqtsu

MECHANIZING PRINCIPIA LOGICO-METAPHYSICA IN FUNCTIONAL TYPE THEORY

DANIEL KIRCHNER, CHRISTOPH BENZMÜLLER, EDWARD N. ZALTA
2019 The Review of Symbolic Logic  
This article reports on recent work in which AOT has been successfully represented and partly automated in the proof assistant system Isabelle/HOL.  ...  This approach enables the fruitful reuse of state-of-the-art higherorder proof assistants, such as Isabelle/HOL, for mechanizing and experimentally exploring challenging logics and theories such as AOT  ...  AOT now uses that notion instead of identity in the formulation of the axioms of free logic. §6. Automation.  ... 
doi:10.1017/s1755020319000297 fatcat:ka5aenuwabgsbnwzrbwve5hsw4

Modelling Value-oriented Legal Reasoning in LogiKEy [article]

Christoph Benzmüller and David Fuenmayor and Bertram Lomfeld
2022 arXiv   pre-print
Modelling value-oriented legal reasoning in that framework, we establish novel bridges between latest research in knowledge representation and reasoning in non-classical logics, automated theorem proving  ...  , and applications in legal reasoning.  ...  This approach also allows us 'upgrade' our object logic whenever necessary. In fact, we add quantifiers and conditionals to  in §5.4.  ... 
arXiv:2006.12789v5 fatcat:5hmrok7ls5c6riplcn3v5gvb34

Embedding and Automating Conditional Logics in Classical Higher-Order Logic [article]

Christoph Benzmueller and Dov Gabbay and Valerio Genovese and Daniele Rispoli
2011 arXiv   pre-print
This embedding enables the application of off-the-shelf higher-order automated theorem provers and model finders for reasoning within and about conditional logics.  ...  A sound and complete embedding of conditional logics into classical higher-order logic is presented.  ...  Acknowledgments: We thank the developers and contributors of the TPTP THF infrastructure and the implementors of the theorem provers and model finders employed in this work.  ... 
arXiv:1106.3685v3 fatcat:ccoew3lqljadhaxq4yyzcax3qa

Universal Reasoning, Rational Argumentation and Human-Machine Interaction [article]

Christoph Benzmüller
2017 arXiv   pre-print
Classical higher-order logic, when utilized as a meta-logic in which various other (classical and non-classical) logics can be shallowly embedded, is well suited for realising a universal logic reasoning  ...  In the future, universal logic reasoning in combination with appropriate, controlled forms of rational argumentation may serve as a communication layer between humans and intelligent machines.  ...  This includes (in alphabetical order): Larry Paulson, Dana Scott, Geoff Sutcliffe, Alexander Steen, Max Wisniewski, Bruno Woltzenlogel-Paleo and Edward Zalta.  ... 
arXiv:1703.09620v1 fatcat:4kybqxjisvdnvfrrsvpxabcomi

Quantified Conditional Logics are Fragments of HOL [article]

Christoph Benzmueller, Valerio Genovese
2012 arXiv   pre-print
A semantic embedding of (constant domain) quantified conditional logic in classical higher-order logic is presented.  ...  Conditional Logics in HOL Quantified conditional logic formulas are identified with certain HOL terms (predicates) of type i o.  ...  In previous work we have studied related embeddings in HOL, including propositional conditional logics [3] and quantified multimodal logics [5] .  ... 
arXiv:1204.5920v1 fatcat:mcvld2mrqvcp3gyhzm4jw3zcty

Embedding and automating conditional logics in classical higher-order logic

Christoph Benzmüller, Dov Gabbay, Valerio Genovese, Daniele Rispoli
2012 Annals of Mathematics and Artificial Intelligence  
This embedding enables the application of off-the-shelf higher-order automated theorem provers and model finders for reasoning within and about conditional logics.  ...  A sound and complete embedding of conditional logics into classical higher-order logic is presented.  ...  Acknowledgments: We thank the developers and contributors of the TPTP THF infrastructure and the implementors of the theorem provers and model finders employed in this work.  ... 
doi:10.1007/s10472-012-9320-z fatcat:vaqujhbg3nagnm2teabyefrxta

The Higher-Order Prover Leo-II

Christoph Benzmüller, Nik Sultana, Lawrence C. Paulson, Frank Theiß
2015 Journal of automated reasoning  
In that section it is also explained why Leo-II (and other THF0 compliant provers) can readily be used for automating a wide spectrum of quantified non-classical logics via semantic embeddings.  ...  Leo-II is an automated theorem prover for classical higher-order logic.  ...  Arnaud Fietzke contributed to code in early phases of the project, and Chad Brown, who shared some Satallax code with Leo-II, has always been a good collaborator of the project.  ... 
doi:10.1007/s10817-015-9348-y pmid:30174358 pmcid:PMC6109767 fatcat:35dv765knbdsjnvfi6ihgbjhha

Higher-order aspects and context in SUMO

Christoph Benzmüller, Adam Pease
2012 Journal of Web Semantics  
A solution is proposed that maps SUMO to quantified multimodal logic which is in turn modeled as a fragment of classical higher-order logic.  ...  This way automated higher-order theorem provers can be safely applied for reasoning about modal contexts in SUMO.  ...  Mapping SUMO via QML to THF0 Exploiting the above embedding of quantified multimodal logic in HOL we can now suitably map SUMO problems via quantified multimodal logics to THFO.  ... 
doi:10.1016/j.websem.2011.11.008 fatcat:vml7qpbtg5fwziok2ehvgw6ynq

Fast LCF-Style Proof Reconstruction for Z3 [chapter]

Sascha Böhme, Tjark Weber
2010 Lecture Notes in Computer Science  
We present independent reconstruction of these proofs in the theorem provers Isabelle/HOL and HOL4 with particular focus on efficiency.  ...  Detailed performance data shows that LCF-style proof reconstruction can be faster than proof search in Z3.  ...  [11] describe a combination of HOL Light and CVC Lite for quantifier-free first-order logic with equality, arrays and linear real arithmetic.  ... 
doi:10.1007/978-3-642-14052-5_14 fatcat:yvi5yovfijayhmc6nnkj34mfju
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