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Grounding Formulas with Complex Terms
[chapter]

2011
*
Lecture Notes in Computer Science
*

We describe the extension of this method to

doi:10.1007/978-3-642-21043-3_2
fatcat:iysh54zqfzaqpl3yq3uggda2me
*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. ...##
###
Quantum Enhanced Inference in Markov Logic Networks

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

doi:10.1038/srep45672
pmid:28422093
pmcid:PMC5395824
fatcat:22gump3aijbplhqyetxrxe75qm
*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. ...##
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Enfragmo: A System for Modelling and Solving Search Problems with Logic
[chapter]

2012
*
Lecture Notes in Computer Science
*

It supports natural specification of problems by providing users

doi:10.1007/978-3-642-28717-6_4
fatcat:4rakb6ysr5ckji6unmce7tvd5u
*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*. ...##
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Complexity of Bose-Hubbard Model : Quantum Phase Transition
[article]

2022
*
arXiv
*
pre-print

For the

arXiv:2112.13066v2
fatcat:cf5f2xlcczh6jcpvtivvdlyrui
*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. ...##
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On constructing a logic for the notion of complete and immediate formal grounding

2016
*
Synthese
*

formal

doi:10.1007/s11229-016-1265-z
fatcat:4mikdtguvjg3nbyhyzdjkwnwda
*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. ...##
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On defining the notion of complete and immediate formal grounding

2015
*
Synthese
*

Let us now consider whether a definition of

doi:10.1007/s11229-015-0923-x
fatcat:bxr67nyuofdkxozeovqdelvitu
*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. ...##
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NUMERICAL EVALUATION OF SELF AND MUTUAL EARTH RETURN IMPEDANCES

2014
*
Carpathian Journal of Electrical Engineering
*

The paper presents an evaluation of analytical self and mutual impedances

doaj:4daeed11881748e2ad6d21a7df931421
fatcat:a4suec32ubhwheqmizrzj2yuo4
*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*. ...##
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Toward a generalization of the logic of grounding

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 ...

##
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BOLZANO'S CONCEPT OF GROUNDING (ABFOLGE) AGAINST THE BACKGROUND OF NORMAL PROOFS

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 ...

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

2013
*
Journal of Modern Physics
*

A

doi:10.4236/jmp.2013.41016
fatcat:tvszmjymmjdsnmncncbub3o4wm
*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 ...##
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Reducing the Complexity of Quantified Formulas via Variable Elimination
[article]

2014
*
arXiv
*
pre-print

Universally quantified variables

arXiv:1408.0700v1
fatcat:iynzntuaffh5bh3uhfwbznkhhu
*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. ...##
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Decidability and complexity of simultaneous rigid E-unification with one variable and related results

2000
*
Theoretical Computer Science
*

Together

doi:10.1016/s0304-3975(98)00185-6
fatcat:boefe4gcbzhmvk7y7rqrioehuq
*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. ...##
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On the complexity of unification and disunification in commutative idempotent semigroups
[chapter]

1997
*
Lecture Notes in Computer Science
*

After this, we analyze the computational

doi:10.1007/bfb0017446
fatcat:2gbm6myfavhjtltjswcilbzyja
*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*. ...##
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On Different Structure-preserving Translations to Normal Form

1996
*
Journal of symbolic computation
*

In this paper, we compare different definitional transformations into normal form

doi:10.1006/jsco.1996.0044
fatcat:nn2ls6cjlrbcfgcmacveels5oi
*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*...##
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An Efficient Decision Procedure for Imperative Tree Data Structures
[chapter]

2011
*
Lecture Notes in Computer Science
*

We further show that satisfiability of

doi:10.1007/978-3-642-22438-6_36
fatcat:55pxk2vqqrfg7omdklsn3zgxti
*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*. ...
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