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Deciding the Word Problem for Ground Identities with Commutative and Extensional Symbols [chapter]

Franz Baader, Deepak Kapur
2020 Lecture Notes in Computer Science  
The word problem for a finite set of ground identities is known to be decidable in polynomial time, and this is also the case if some of the function symbols are assumed to be commutative.  ...  In addition, we investigate a variant of extensionality that is more appropriate for commutative function symbols, but which raises the complexity of the word problem to coNP.  ...  The authors would like to thank the reviewers for their careful reading of the paper and their useful comments, which helped to improve the presentation of the paper.  ... 
doi:10.1007/978-3-030-51074-9_10 fatcat:7o3g6hd3wvejzbelngkci4dzyq

A Local Graph-rewriting System for Deciding Equality in Sum-product Theories

José Bacelar Almeida, Jorge Sousa Pinto, Miguel Vilaça
2007 Electronical Notes in Theoretical Computer Science  
In this paper we give a graph-based decision procedure for a calculus with sum and product types.  ...  Although our motivation comes from the Bird-Meertens approach to reasoning algebraically about functional programs, the language used here can be seen as the internal language of a category with binary  ...  theory E, and (ii) an algorithm is given for deciding equality under E.  ... 
doi:10.1016/j.entcs.2006.10.031 fatcat:hdnmaivokfch5bckgrtl2ncmhm

Uniform Derivation of Decision Procedures by Superposition [chapter]

Alessandro Armando, Silvio Ranise, Michaël Rusinowitch
2001 Lecture Notes in Computer Science  
arrays and combinations of them.  ...  We show how a well-known superposition-based inference system for first-order equational logic can be used almost directly as a decision procedure for various theories including lists, arrays, extensional  ...  Note that the word problem for ground Associative-Commutative (AC) theories is decidable [NR91] but for ground AC+Distributivity is undecidable[Mar92].  ... 
doi:10.1007/3-540-44802-0_36 fatcat:ngf5cmzscfeatbql2pkjbk6esi

On a Rewriting Approach to Satisfiability Procedures: Extension, Combination of Theories and an Experimental Appraisal [chapter]

Alessandro Armando, Maria Paola Bonacina, Silvio Ranise, Stephan Schulz
2005 Lecture Notes in Computer Science  
, lists, arrays with and without extensionality, sets with extensionality and the combination of lists and arrays.  ...  CVC and CVC Lite seem to be the only state-of-the-art tools implementing a correct and complete procedure for arrays with extensionality. 1 Contrary to expectation, the general first-order prover with  ...  We thank Stefano Ferrari, former student of the second author, for running preliminary experiments, and Paolo Fiorini, colleague of the second author, for access to the computers of the robotics laboratory  ... 
doi:10.1007/11559306_4 fatcat:mar73gtjkzhcne5scewq6xi2su

Conservative Intensional Extension of Tarski's Semantics

Zoran Majkić
2013 Advances in Artificial Intelligence  
algebra of concepts, and, successively, into an extensional relational algebra (different from Cylindric algebras).  ...  Then we show that this composition corresponds to the Tarski's interpretation of the standard extensional FOL in this possible world.  ...  We will use '=' for the extensional identity for relations in R.  ... 
doi:10.1155/2013/920157 fatcat:lgezrcimsrbiff6qcu2zj75ie4

Intensionality and Two-steps Interpretations [article]

Zoran Majkic
2011 arXiv   pre-print
of concepts, and, successively, to the new extensional relational algebra (different from Cylindric algebras).  ...  In the case of the pure FOL we obtain commutative homomorphic diagram that holds in each given possible world of the intensional FOL, from the free algebra of the FOL syntax, toward its intensional algebra  ...  We will use '=' for the extensional identity for relations in R.  ... 
arXiv:1103.0967v1 fatcat:pxuo5gtzxbe4jfg6lh65f3ty5m

A rewriting approach to satisfiability procedures

Alessandro Armando, Silvio Ranise, Michaël Rusinowitch
2003 Information and Computation  
arrays, extensional finite sets, and combinations of them.  ...  We show how a well-known superposition-based inference system for first-order equational logic can be used almost directly for deciding satisfiability in various theories including lists, encryption, extensional  ...  Kapur and R. Nieuwenhuis for their comments. The anonymous referees helped improving the paper.  ... 
doi:10.1016/s0890-5401(03)00020-8 fatcat:zywt7ebhmnbj3fki25gss65hwq

Towards lean proof checking [chapter]

G. Barthe, H. Elbers
1996 Lecture Notes in Computer Science  
systems and the computational power of term rewriting systems, provide a suitable environment for theorem proving.  ...  Besides, our work provides the rst attempt to combine symbolic computation systems with theorem provers such as Coq and Lego, which are based on intensional type theories.  ...  De ne a commutator x; y] = d x y ? y x. We will prove that 8x; y; z 2 R: x; y; z]]+ y; z; x]] + z; x; y]] = 0 (Jacobi identity) holds.  ... 
doi:10.1007/3-540-61697-7_5 fatcat:uouivor7kndd7kqk7rb6veyiyq

First-order Logic: Modality and Intensionality [article]

Zoran Majkic
2011 arXiv   pre-print
), with the two-step interpretation of the FOL that eliminates the weak points of the Montague's intensional semantics.  ...  intensional algebra of concepts, and, successively, to the new extensional relational algebra (different from Cylindric algebras), and we show that it corresponds to the Tarski's interpretation of the  ...  We will use '=' for the extensional identity for relations in R.  ... 
arXiv:1103.0680v1 fatcat:u7rfq4pyz5eabebisstahipnbq

New results on rewrite-based satisfiability procedures

Alessandro Armando, Maria Paola Bonacina, Silvio Ranise, Stephan Schulz
2009 ACM Transactions on Computational Logic  
If a sound and complete inference system for first-order logic is guaranteed to terminate on T-satisfiability problems, any theorem-proving strategy with that system and a fair search plan is a T-satisfiability  ...  Program analysis and verification require decision procedures to reason on theories of data structures. Many problems can be reduced to the satisfiability of sets of ground literals in theory T.  ...  ACKNOWLEDGMENTS We thank Mnacho Echenim for several suggestions to improve preliminary versions of this article, and especially for helping us correcting the proofs of Section 3.2.  ... 
doi:10.1145/1459010.1459014 fatcat:q7ztkpc4lfbhzmkywvpk7fitoa

Equational Logic and Rewriting [chapter]

Claude Kirchner, Hélène Kirchner
2014 Handbook of the History of Logic  
Ground reducibility is decidable for finite rewrite systems [87, 126] and is EXPTIME-complete in the general case [35] .  ...  The latter property is decidable for a confluent and terminating rewrite system.  ... 
doi:10.1016/b978-0-444-51624-4.50006-x fatcat:eqtvr66m65eula7otl7fr6ppaa

On Wittgenstein's transcendental deductions

Russell Connelly
2017 Belgrade Philosophical Annual  
I show how these two, crucial claims are both demonstrated and subsequently deployed by Wittgenstein within a series of transcendental deductions, a series which begins with extensionalism as a generalized  ...  Specifically, the claims are of the logical independence of elementary propositions, and that infinity is a number.  ...  Its purpose is to show that, if α is any argument for which 'φα' is significant, i.e., for which we have φα v ~ φα, then 'φx' is significant when, and only when, x is either identical with α or not identical  ... 
doi:10.5937/bpa1730151c fatcat:wpstytwtrraexe3hfxtwcbwqsm

To Be F Is To Be G

Cian Dorr
2016 Philosophical Perspectives  
is ambiguous, so that Indiscriminability has both true and false readings. case to be made for strengthening it to an identification: 27 The Identity Identity ≡ ≡ ⟨ , ⟩ .∀ ⟨ ⟩ ( ( ) ↔ ( )) In words: identification  ...  and disjunction operators ∧ andfor both finite and transfinite ordinals , the natural generalisations of commutativity and associativity will be inconsistent with the natural generalisation of OLC.  ...  (b) There is a populated, extensionally full ℐ Log -model in which each z ∈ is either noncircular or identical to ⟦ ⟧ for some closed term of ℐ Neg , and in which ⟦ .¬(¬ )⟧ → = ⟦ . ⟧ → .  ... 
doi:10.1111/phpe.12079 fatcat:jokqyehg6feergtrfojdbclmbm

Polarised Intermediate Representation of Lambda Calculus with Sums

Guillaume Munch-Maccagnoni, Gabriel Scherer
2015 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science  
The theory of the -calculus with extensional sums is more complex than with only pairs and functions.  ...  We offer an introduction from the ground up to our approach, and we review the benefits.  ...  Many thanks to Pierre-Évariste Dagand, Olivier Danvy, Tim Griffin, Adrien Guatto, Thomas Streicher, Noam Zeilberger, and the anonymous reviewers, for their comments, criticisms and suggestions.  ... 
doi:10.1109/lics.2015.22 dblp:conf/lics/Munch-Maccagnoni15 fatcat:rsuvx3pj35ec3of7xax5nzuv4e

Book Review: Principia Mathematica

James Byrnie Shaw
1912 Bulletin of the American Mathematical Society  
For example, it is not easy to decide what the authors mean by extensional.  ...  Under the limitations to the use of these symbols we find that, while x is always identical with x y yet the round square is not identical with the round square, for the reason there is no round square  ... 
doi:10.1090/s0002-9904-1912-02233-4 fatcat:ulldildqrnerpk6n5kycdw7asq
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