421,474 Hits in 5.0 sec

Grounding Formulas with Complex Terms [chapter]

Amir Aavani, Xiongnan Wu, Eugenia Ternovska, David Mitchell
2011 Lecture Notes in Computer Science  
We describe the extension of this method to ground formulas of first-order logic extended with arithmetic and aggregate operators.  ...  Given a finite domain, grounding is the the process of creating a variablefree first-order formula equivalent to a first-order sentence.  ...  the method described in this paper for formulas with complex terms, for all terms that do not involve the Sum aggregate.  ... 
doi:10.1007/978-3-642-21043-3_2 fatcat:iysh54zqfzaqpl3yq3uggda2me

Quantum Enhanced Inference in Markov Logic Networks

Peter Wittek, Christian Gogolin
2017 Scientific Reports  
We analyze the graph structures that are produced by various lifting methods and investigate the extent to which quantum protocols can be used to speed up Gibbs sampling with state preparation and measurement  ...  Groundings are viewed as connected if they can jointly appear in a grounding of some formula of the knowledge base.  ...  Still, an exponential scaling with the number of all possible groundings of all atoms n remains, and the complexity diverges in the low temperature limit as β goes to infinity.  ... 
doi:10.1038/srep45672 pmid:28422093 pmcid:PMC5395824 fatcat:22gump3aijbplhqyetxrxe75qm

Enfragmo: A System for Modelling and Solving Search Problems with Logic [chapter]

Amir Aavani, Xiongnan Wu, Shahab Tasharrofi, Eugenia Ternovska, David Mitchell
2012 Lecture Notes in Computer Science  
It supports natural specification of problems by providing users with a rich language, based on an extension of first order logic.  ...  Enfragmo takes as input a problem specification and a problem instance and produces a propositional CNF formula representing solutions to the instance, which is sent to a SAT solver.  ...  The formula for each tuple in an answer to a simple term is either True or False. A term which is not simple is called complex.  ... 
doi:10.1007/978-3-642-28717-6_4 fatcat:4rakb6ysr5ckji6unmce7tvd5u

Complexity of Bose-Hubbard Model : Quantum Phase Transition [article]

Wung-Hong Huang
2022 arXiv   pre-print
For the ground state we can find the exact value of complexity which is the summation of all order.  ...  We also study the excited state and present the general formulas of Bose-Hubbard model complexity, which shows a similar form as that in λϕ^4 theory studied in our previous paper.  ...  In fact the formulas (3.44) are the exact values and we can let n → ∞. Note that being able to obtain the exact formula for ground state complexity is a special property in our method.  ... 
arXiv:2112.13066v2 fatcat:cf5f2xlcczh6jcpvtivvdlyrui

On constructing a logic for the notion of complete and immediate formal grounding

Francesca Poggiolesi
2016 Synthese  
formal grounding based on that definition.  ...  Our logic will have the form of a calculus of natural deduction, will be proved to be sound and complete and will allow us to have fine-grained grounding principles.  ...  In more formal terms, the idea here is that the ground for the truth of a formula of the form ¬A is a formula B (satisfying a certain complexity constraint) such that A and B lead to a contradiction.  ... 
doi:10.1007/s11229-016-1265-z fatcat:4mikdtguvjg3nbyhyzdjkwnwda

On defining the notion of complete and immediate formal grounding

Francesca Poggiolesi
2015 Synthese  
Let us now consider whether a definition of grounding in terms of derivability and the notion of being completely and immediately less complex -let us call this definition D-C def -can properly deal with  ...  Thus, if we define formal grounding just in terms of derivability and complexity, we cannot make any distinction between grounds and robust conditions.  ... 
doi:10.1007/s11229-015-0923-x fatcat:bxr67nyuofdkxozeovqdelvitu


Denisa STET, Dan D. MICU, Levente CZUMBIL, Emil SIMION
2014 Carpathian Journal of Electrical Engineering  
The paper presents an evaluation of analytical self and mutual impedances formulas of lines with earth return, taking into account the ground correction terms.  ...  The determined formulas contain semi-infinite integral terms which are calculated by a novel stable and efficient numerical integration scheme in order to overcome the involved oscillation problems.  ...  Introducing in inductances relations the (concept of) skin depth these parameters becomes a complex numbers with terms which represent the energy dissipation in the ground.  ... 
doaj:4daeed11881748e2ad6d21a7df931421 fatcat:a4suec32ubhwheqmizrzj2yuo4

Toward a generalization of the logic of grounding

Francesca Poggiolesi, Nissim Francez
2020 THEORIA : an International Journal for Theory, History and Fundations of Science  
grounding.  ...  Such ground-analysis not only serves to extend the applicability of the logic of grounding but also leads to a generalization of [Poggiolesi, 2016]'s definition of the notion of complete and immediate  ...  The first consists in organizing all formulas of the propositional classical language in a grounding hierarchy: each level of the hierarchy contains formulas of different complexity, with complexity increasing  ... 
doi:10.1387/theoria.21162 fatcat:ixhjfnzizfhgxhkrieqvllqbea


2013 The Review of Symbolic Logic  
Grounding (Abfolge) is an objective ground-consequence relation among true propositions that is explanatory in nature.  ...  In this paper I will provide a thorough discussion and reconstruction of Bernard Bolzano's theory of grounding and a detailed investigation into the parallels between his concept of grounding and current  ...  It is of course possible to measure the complexity of a formula in terms of its atomic subformulas. 67 In this line, we could define the atomic content of a formula as the collection of all occurrences  ... 
doi:10.1017/s1755020313000154 fatcat:aniegf44fbaxnfcm7nuc5kn2l4

Electric Multipole Polarizabilities of Quantum Bound Systems in the Transition Matrix Formalism

Vladyslav F. Kharchenko
2013 Journal of Modern Physics  
A formula for the multipole polarizabilities of a two-body bound complex formed by a central interaction potential has been derived and studied.  ...  spectrum; instead, it makes possible to calculate the polarizability of a few-body bound complex directly based on solving integral equations for the wave function of the ground bound state and the transition  ...  The general Formula (12) for the electric multipole polarizability of a bound complex of particles N   1, 2, , N  0 contains the ground-state wave function  and "truncated" propagator        ... 
doi:10.4236/jmp.2013.41016 fatcat:tvszmjymmjdsnmncncbub3o4wm

Reducing the Complexity of Quantified Formulas via Variable Elimination [article]

Aboubakr Achraf El Ghazi and Mattias Ulbrich and Mana Taghdiri and Mihai Herda
2014 arXiv   pre-print
Universally quantified variables with a finite set of sufficient ground terms can be eliminated by instantiating them with the computed ground terms.  ...  The simplification is based on an analysis of the ground terms occurring as arguments in function applications.  ...  Depending on the complexity of the involved terms, this may introduce additional overhead for the solver.  ... 
arXiv:1408.0700v1 fatcat:iynzntuaffh5bh3uhfwbznkhhu

Decidability and complexity of simultaneous rigid E-unification with one variable and related results

Anatoli Degtyarev, Yuri Gurevich, Paliath Narendran, Margus Veanes, Andrei Voronkov
2000 Theoretical Computer Science  
Together with a previous result regarding the undecidability of the ∃∃-fragment, we obtain a complete classiÿcation of decidability of the prenex fragment of intuitionistic logic with equality, in terms  ...  Moreover, we consider a case of SREU where one allows several variables, but each rigid equation either contains one variable, or has a ground left-hand side and an equality between two variables as a  ...  Terms and formulas Terms and formulas are deÿned in the standard manner. We refer to terms and formulas collectively as expressions.  ... 
doi:10.1016/s0304-3975(98)00185-6 fatcat:boefe4gcbzhmvk7y7rqrioehuq

On the complexity of unification and disunification in commutative idempotent semigroups [chapter]

Miki Hermann, Phokion G. Kolaitis
1997 Lecture Notes in Computer Science  
After this, we analyze the computational complexity of the decision problem for elementary ground ACI-disuni cation.  ...  Finally, we study the computational complexity of a restricted version of elementary ACI-matching, which arises naturally as a set-term matching problem in the context of the logic data language LDL.  ...  of variables by ground terms.  ... 
doi:10.1007/bfb0017446 fatcat:2gbm6myfavhjtltjswcilbzyja

On Different Structure-preserving Translations to Normal Form

1996 Journal of symbolic computation  
In this paper, we compare different definitional transformations into normal form with respect to the Herbrand complexity of the resulting normal forms.  ...  We identify a sequence of formulae H 1 , H 2 , . . ., for which the difference of the Herbrand complexity of the different translations of H k is bounded from below by a non-elementary function in k.  ...  We will use the term "classical" or "traditional" transformations into normal form for translations which first transform a closed first-order formula into a negation normal form, i.e., a formula with  ... 
doi:10.1006/jsco.1996.0044 fatcat:nn2ls6cjlrbcfgcmacveels5oi

An Efficient Decision Procedure for Imperative Tree Data Structures [chapter]

Thomas Wies, Marco Muñiz, Viktor Kuncak
2011 Lecture Notes in Computer Science  
We further show that satisfiability of formulas in TREX is decidable in NP.  ...  The low complexity makes it an attractive alternative to more expensive logics such as monadic second-order logic (MSOL) over trees, which have been traditionally used for reasoning about tree data structures  ...  In fact TREX formulas can be expressed in terms of MSOL formulas with at most two quantifier alternations, which gives a 2-EXPTIME upper-bound for the complexity.  ... 
doi:10.1007/978-3-642-22438-6_36 fatcat:55pxk2vqqrfg7omdklsn3zgxti
« Previous Showing results 1 — 15 out of 421,474 results