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On Reductions of Hintikka Sets for Higher-Order Logic [article]

Alexander Steen, Christoph Benzmüller
2021 arXiv   pre-print
Steen's (2018) Hintikka set properties for Church's type theory based on primitive equality are reduced to the Hintikka set properties of Brown (2007).  ...  Using this reduction, a model existence theorem for Steen's properties is derived.  ...  We thank an anonymous reviewer for very valuable feedback to this work (cf. footnote 1).  ... 
arXiv:2004.07506v3 fatcat:czsfrf5lfbgzllkc2tzqzkhzxe

Page 6166 of Mathematical Reviews Vol. , Issue 94k [page]

1994 Mathematical Reviews  
Sandu’s distinction between the so-called “standard” and “non- standard” interpretations of higher-order logic.  ...  What the authors do not note in this context is that, for Frege, classes are not sets in the sense of the iterative hierarchy of ZF set theory, which is the basis and assumed framework of Hintikka and  ... 

JAAKKO HINTIKKA 1929–2015

JOUKO VÄÄNÄNEN
2015 Bulletin of Symbolic Logic  
Another early but far-reaching contribution of Hintikka is the reduction of the theory of finite types (i.e., higher order logic) to a fragment of second order logic [10].  ...  With his Independence Friendly Logic [17], which is equivalent in expressive power to the existential fragment of second order logic, Hintikka came back to this reduction in the 90s.  ... 
doi:10.1017/bsl.2015.35 fatcat:vwqjwmv4knfr5dzxkx7nm76pva

Experiments in Theorem Proving for Topological Hybrid Logic

Dmitry Sustretov, Guillaume Hoffmann, Carlos Areces, Patrick Blackburn
2009 Electronical Notes in Theoretical Computer Science  
The second is a translation-based approach that makes use of HyLoTab [18], a tableaux-based theorem prover for hybrid logic under the standard relational interpretation.  ...  We compare the two methods, and note a number of directions for further work.  ...  The Hintikka sets on the board. The order in the list matters: the tail of the list is the latest Hintikka set added.  ... 
doi:10.1016/j.entcs.2009.02.043 fatcat:nz7enhcnojbspioof6gqy2o2ym

Page 6 of Mathematical Reviews Vol. 35, Issue 1 [page]

1968 Mathematical Reviews  
One of the results given in the paper (at the top of page 1273) is a restatement of the well-known theorem of Hintikka concerning the ‘“‘reduction”’ of nth-order formulae to second-order ones [see J.  ...  All theorems announced in this paper are concerned with logical formulae of higher order.  ... 

Page 84 of American Mathematical Society. Transactions of the American Mathematical Society Vol. 92, Issue 1 [page]

1959 American Mathematical Society. Transactions of the American Mathematical Society  
Hintikka, Reductions in the theory of types, Acta Philos. Fenn, (1955) pp. 61-115. 5. A. Mostowski, On absolute properties of relations, J. Symb. Logic vol. 12 (1947) pp. 33-42. 6. A.  ...  On the other hand a formula in which all terms are of order at most one is set-persistent if and only if it is strongly standard increasing.  ... 

Page 84 of American Mathematical Society. Transactions of the American Mathematical Society Vol. 92, Issue 1 [page]

1959 American Mathematical Society. Transactions of the American Mathematical Society  
Hintikka, Reductions in the theory of types, Acta Philos. Fenn, (1955) pp. 61-115. 5. A. Mostowski, On absolute properties of relations, J. Symb. Logic vol. 12 (1947) pp. 33-42, 6. A.  ...  On the other hand a formula in which all terms are of order at most one is set-persistent if and only if it is strongly standard increasing.  ... 

Reasoning in Fuzzy Description Logics using Automata

Stefan Borgwardt, Rafael Peñaloza
2016 Fuzzy sets and systems (Print)  
Clearly, due to the different semantics in these logics, the construction of the automata for fuzzy DLs is more involved than for the classical case.  ...  The methods vary from deciding emptiness of automata on infinite trees to inclusions between automata on finite words.  ...  Acknowledgements This work was partially supported by the German Research Foundation (DFG) under grant BA 1122/17-1 (FuzzyDL) and within the Cluster of Excellence 'Center for Advancing Electronics Dresden  ... 
doi:10.1016/j.fss.2015.07.013 fatcat:zepnuj6iazcvrndlaradjyafzy

Completeness and Cut-elimination in the Intuitionistic Theory of Types

Mary DeMarco, Jame Lipton
2005 Journal of Logic and Computation  
We extend Andrews' notion of Hintikka sets to intuitionistic higher-order logic in a way that also defines tableau-provability for intuitionistic type theory.  ...  It is a matter of debate to what extent a syntactic proof of cut-elimination has ever been found for higher-order logic.  ...  Acknowledgements The authors wish to express a special debt to Chad Brown of Carnegie-Mellon University for pointing out certain pitfalls in the proof of cut-elimination, and correcting significant errors  ... 
doi:10.1093/logcom/exi055 fatcat:chyc4ac5b5bh5n2ee4fw5rzchy

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  ...  I aim to discuss these, and other points posed by Hintikka, as challenges and opportunities for paraconsistentism, paraconsistent logics and IF logics, as well as to raise some criticisms on Hintikka's  ...  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

Cut-Simulation in Impredicative Logics [chapter]

Christoph E. Benzmüller, Chad E. Brown, Michael Kohlhase
2006 Lecture Notes in Computer Science  
We investigate cut-elimination and cut-simulation in impredicative (higher-order) logics.  ...  This calls for the development of calculi where these principles are built-in instead of being treated axiomatically.  ...  Higher-Order Logic In [5] we have re-examined the semantics of classical higher-order logic with the purpose of clarifying the role of extensionality.  ... 
doi:10.1007/11814771_20 fatcat:kb6ptighknclllcgoqnlojxpoq

Which Mathematical Logic is the Logic of Mathematics?

Jaakko Hintikka
2012 Logica Universalis  
History of Logic vs. History of Mathematics. Jaakko Hintikka. 032012 17 BIBLIOGRAPHY  ...  Acknowledgements This paper was written when Jaakko Hintkkka was a Distinguished Visiting Fellow of the Collegium for Advanced Studies of the University of Helsinki.  ...  to be as a separate set-theoretical or higher-order axiom.  ... 
doi:10.1007/s11787-012-0065-6 fatcat:7egblszkrjg7lmnutjlz2igfqu

Comparative Similarity, Tree Automata, and Diophantine Equations [chapter]

Mikhail Sheremet, Dmitry Tishkovsky, Frank Wolter, Michael Zakharyaschev
2005 Lecture Notes in Computer Science  
For finite subspaces of the real line (and higher dimensional Euclidean spaces) we prove the undecidability of satisfiability by a reduction of the solvability problem for Diophantine equations.  ...  In particular, using a reduction to the emptiness problem for certain tree automata, we show that the satisfiability problem for this logic is ExpTime-complete for the classes of all finite symmetric and  ...  The work on this paper was partially supported by the U.K. EPSRC research grants GR/S61966/01 and GR/S61973/01.  ... 
doi:10.1007/11591191_45 fatcat:hjn4pwlroffbjo2jyluhmd7zqe

Beyond knowing that: a new generation of epistemic logics [article]

Yanjing Wang
2016 arXiv   pre-print
Epistemic logic has become a major field of philosophical logic ever since the groundbreaking work by Hintikka (1962).  ...  We survey our recent line of work on the epistemic logics of "knowing whether", "knowing what" and "knowing how" to demonstrate the use of this new approach.  ...  The author is grateful to Hans van Ditmarsch for his very detailed comments on an early version of this paper.  ... 
arXiv:1605.01995v3 fatcat:n2vpwbpkafflxfzkjwl7lnaqzm

Blocking Automata for PSPACE DLs

Franz Baader, Jan Hladik, Rafael Peñaloza
2007 International Workshop on Description Logics  
Whereas tableau-based algorithms usually yield worst-case optimal algorithms in the case of PSpace-complete logics, it is often very hard to design optimal tableau-based algorithms for ExpTime-complete  ...  In the present paper, we formulate conditions under which an on-the-fly construction of such an exponentially large automaton can be used to obtain a PSpace-algorithm.  ...  For our reduction this implies that the automaton we construct for a given input C, T does not actually accept the Hintikka trees for C, T .  ... 
dblp:conf/dlog/BaaderHP07 fatcat:vio7t4nuhfenjjiw5nb3zeohki
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