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Bringing them all Together

C. Areces
2001 Journal of Logic and Computation  
Acknowledgements First of all we want to thank our anonymous reviewers for their helpful and often very detailed comments.  ...  Finally, we'd like to thank Dov Gabbay for letting us put this special issue together.  ...  Direct Modal, Description and Hybrid Resolution. One of the reasons for hybridizing a modal logic is to try to improve its computational behavior.  ... 
doi:10.1093/logcom/11.5.657 fatcat:vaqismzq2zas7pqssvyepaht6m

Simulation and Synthesis of Deduction Calculi

Renate A. Schmidt
2010 Electronical Notes in Theoretical Computer Science  
One approach is based on simulating deduction approaches with techniques of automated reasoning and first-order resolution.  ...  This paper gives an overview of two methods for automatically or semi-automatically generating deduction calculi from the semantic specification of a logic.  ...  In first-order resolution an important notion is redundancy elimination.  ... 
doi:10.1016/j.entcs.2010.04.016 fatcat:pl77knopnzbx7ggugkxqyo2xi4

Constraint model elimination and a PTTP-implementation [chapter]

Peter Baumgartner, Frieder Stolzenburg
1995 Lecture Notes in Computer Science  
In constraint logic programming, proof procedures for Horn clauses are enhanced with an interface to efficient constraint solvers.  ...  The Lion and Unicorn puzzle is stated as problem 45 in [Smu natural language description of the problem is as follows. § d enotes the logical exclusive or.  ...  Acknowledgements We would like to thank Franz Baader, Jürgen Dix, Ulrich Furbach, Thom Frühw chael Kühn, Olaf Menkens and Joachim Niehren for helpful discussions and c on this paper.  ... 
doi:10.1007/3-540-59338-1_37 fatcat:n2fuu46555fidb3zjpkl4sbuyq

Building Rules on Top of Ontologies for the Semantic Web with Inductive Logic Programming

2008 Theory and Practice of Logic Programming  
It is intended to follow the tradition of hybrid knowledge representation and reasoning systems, such as$\mathcal{AL}$-log that integrates the description logic$\mathcal{ALC}$and the function-free Horn  ...  Yet, for illustrative purposes, we also discuss an instantiation of the framework which aims at description and turns out to be useful in Ontology Refinement.  ...  Reasoning for AL-log knowledge bases is based on constrained SLD-resolution, i.e. an extension of SLD-resolution with a tableau calculus for ALC to deal with constraints.  ... 
doi:10.1017/s1471068407003195 fatcat:2ncsy2pl35holhip7j5xdtgcam

Page 7144 of Mathematical Reviews Vol. , Issue 95m [page]

1995 Mathematical Reviews  
The work is carried out in an extension of logical frameworks, a system in which proofs are represented by terms in a typed A-calculus.  ...  In outline, it proceeds by first looking for a term which can be expressed as a recursion term (standing for a proof which has the correct form to be an expansion of the first few cases of an induction  ... 

An order-sorted resolution in theory and practice

Trudy Weibel
1997 Theoretical Computer Science  
On the theoretical side, the necessary foundations are laid, ranging from syntax and semantics of the order-sorted first-order predicate logic to a completeness theorem for the calculus.  ...  The originality of this work lies in realising such an upgrade.  ...  Acknowledgements I would like to thank the anonymous referees and the editor for many helpful suggestions.  ... 
doi:10.1016/s0304-3975(97)00051-0 fatcat:tzaakwa7h5e25is7qcohmpjc4y

Modal Hybrid Logic

Andrzej Indrzejczak
2007 Logic and Logical Philosophy  
In the first part a variety of hybrid languages and logics is presented with a discussion of expressivity matters.  ...  The main point is to show that application of hybrid logics may remarkably improve the situation in modal proof theory.  ...  Below we describe briefly the extension of propositional hybrid logic to first-order modal hybrid logic.  ... 
doi:10.12775/llp.2007.006 fatcat:emmg3cw7nfgepckawq634p7lky

Resolution in Modal, Description and Hybrid Logic

C. Areces
2001 Journal of Logic and Computation  
We provide a resolution-based proof procedure for modal, description and hybrid logic that improves on previous proposals in important ways.  ...  In addition, by using the hybrid machinery it avoids the complexities of earlier propositional resolution-based methods for modal logic.  ...  Maarten de Rijke was supported by the Spinoza project 'Logic in Action' and by a grant from the Netherlands Organization for Scientific Research (NWO) under project numbers 612-13-001, 365-20-005, 612.069.006  ... 
doi:10.1093/logcom/11.5.717 fatcat:4uwqbmihpbcmpbn5v4vbevsz2a

On the practical value of Herbrand disjunctions

Uwe Petermann
2004 Logic and Logical Philosophy  
Herbrand disjunctions are a means for reducing the problem of whether a first-oder formula is valid in an open theory T or not to the problem whether an open formula, one of the so called Herbrand disjunctions  ...  in theories into automatic theorem provers [26] .  ...  We use this examples in order to illustrate automated reasoning in this logic. For this purpose we use a two-step translation of this logic into first-order logic.  ... 
doi:10.12775/llp.2000.009 fatcat:dbczodvuvnd4lcd2clctw4vdqe

Special issue on 'Logical frameworks and metalanguages'

2003 Journal of functional programming  
The first actual attempts at mechanisation of logical reasoning through the resolution principle (automated theorem proving) had been disappointing, but their shortcomings gave rise to a considerable body  ...  Meanwhile, computer modelling developed a need for concrete uses of logic, first for the design of computer circuits, then more widely for increasing the reliability of sofware through the use of formal  ...  They describe a mechanisable proposal for higher order abstract syntax on a significant case study for π-calculus, an important distributed process calculus.  ... 
doi:10.1017/s0956796802004549 fatcat:zkmf6ncdjnhbvfhmshmsevmvt4

Page 739 of Mathematical Reviews Vol. , Issue 2001B [page]

2001 Mathematical Reviews  
Gilmore, Partial functions in an impredicative simple theory of types (186-201); Jean Goubault- Larrecq, A simple sequent system for first-order logic with free constructors (202-216); Heiko Mantel and  ...  calculus for pro- noun resolution (247-262); Heribert Schiitz, Generating minimal Herbrand models step by step (263-277); Miroslava Tzakova, Tableau calculi for hybrid logics (278-292); Claus-Peter Wirth  ... 

Basic research in computer science and software engineering at SKLCS

Jian Zhang, Wenhui Zhang, Naijun Zhan, Yidong Shen, Haiming Chen, Yunquan Zhang, Yongji Wang, Enhua Wu, Hongan Wang, Xueyang Zhu
2008 Frontiers of Computer Science in China  
The research topics of the laboratory include: concurrency theory, theory and algorithms for real-time systems, formal specifications based on context-free grammars, semantics of programming languages,  ...  model checking, automated reasoning, logic programming, software testing, software process improvement, middleware technology, parallel algorithms and parallel software, computer graphics and human-computer  ...  resolution, decidability of a class of theory, satisfiability problems in the propositional logic and the first-order logic, and so on.  ... 
doi:10.1007/s11704-008-0001-3 fatcat:zgeczciftbc47o5atyg27ingvi

Formalizing a Seligman-Style Tableau System for Hybrid Logic [chapter]

Asta Halkjær From, Patrick Blackburn, Jørgen Villadsen
2020 Lecture Notes in Computer Science  
Hybrid logic is modal logic enriched with names for worlds. We formalize soundness and completeness proofs for a Seligman-style tableau system for hybrid logic in the proof assistant Isabelle/HOL.  ...  Moreover, the completeness proof we formalize is synthetic which suggests we can extend this work to prove a wider range of results about hybrid logic.  ...  [3] , a Hilbert system for epistemic logic [12] , and the first-order resolution calculus [21] .  ... 
doi:10.1007/978-3-030-51074-9_27 fatcat:klxbbkjmwzhh7kfxm365meu4ai

Theorem proving with built-in hybrid theories

Uwe Petermann
2004 Logic and Logical Philosophy  
The approach is demonstrated by its application to the target calculi of the algebraic translation [9] of multi-modal and extended multi-modal [7] logic to first-order logic.  ...  The paper formulates sufficient criteria for the construction of complete calculi which enable reasoning under hybrid theories combined from sub-theories.  ...  Many improvements of resolution have been shown as special kinds of theory resolution in [22] . For a treatment of the lifting to the full first-order calculus see [1] or [19] .  ... 
doi:10.12775/llp.1998.005 fatcat:l3q7j6e22zgnnb6tvywcnkpm6u

Page 3178 of Mathematical Reviews Vol. , Issue 2003e [page]

2003 Mathematical Reviews  
In this paper, the authors present a “basic” theory, that is, a theory which has “a first essentially finitary nucleus, and a second part useful in obtaining a good degree of self-description”.  ...  Summary: “We present an algorithm, based both on semantic tableaux and resolution, which is able to check the projectivity (exactness) of a formula in intuitionistic propositional calculus.  ... 
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