Filters








35,212 Hits in 6.6 sec

Finding Finite Models in Multi-Sorted First Order Logic [article]

Giles Reger, Martin Suda, Andrei Voronkov
2016 arXiv   pre-print
This work extends the existing MACE-style finite model finding approach to multi-sorted first order logic.  ...  first order logic.  ...  We use monotonic sorts introduced in [4] in a new way for the multi-sorted case to reduce the search space further (Sect. 5.5). 3.  ... 
arXiv:1604.08040v1 fatcat:3mwe45k45fb5lefbu53sfouupi

Expressive power and abstraction in Essence

David G. Mitchell, Eugenia Ternovska
2008 Constraints  
Development of languages for specifying or modelling problems is an important direction in constraint modelling.  ...  Our study is an application of descriptive complexity theory, and illustrates the value of taking a logic-based view of modelling and specification languages.  ...  order logic whose finite models are exactly the (un-sorted versions of the) structures in K Γ .  ... 
doi:10.1007/s10601-008-9050-3 fatcat:dg64v3pux5gs5pxxxljiqgwl5y

Non-cyclic Sorts for First-Order Satisfiability [chapter]

Konstantin Korovin
2013 Lecture Notes in Computer Science  
We implemented our finite model finding translation in iProver and evaluated it over the TPTP library.  ...  In this paper we investigate the finite satisfiability problem for firstorder logic.  ...  Introduction Currently, the most successful methods for finite model finding in first-order logic are based on exhaustive flattening of function terms [3, 10] .  ... 
doi:10.1007/978-3-642-40885-4_15 fatcat:qrsnrwxiuzbfpn3hwjvydmuhgq

ALGEBRAIC LOGIC AND LOGICALLY-GEOMETRIC TYPES IN VARIETIES OF ALGEBRAS

BORIS PLOTKIN, ELENA ALADOVA, EUGENE PLOTKIN
2013 Journal of Algebra and its Applications  
We show that types appear naturally as logical kernels in the Galois correspondence between filters in the Halmos algebra of first order formulas with equalities and elementary sets in the corresponding  ...  These ties go back and forth from universal algebraic geometry to the model theory through the machinery of algebraic logic.  ...  For instance, we need multi-sorted variant of Halmos algebras in order to work with finite dimensional affine spaces and to construct geometry related to first order calculus in arbitrary Θ.  ... 
doi:10.1142/s0219498812501460 fatcat:w2g2zehnobd6zl4mtwyg3n7zgi

Solving Constrained Horn Clauses over ADTs by Finite Model Finding [article]

Yurii Kostyukov, Dmitry Mordvinov, Grigory Fedyukovich
2021 arXiv   pre-print
First-order logic is a natural way of expressing the properties of computation, traditionally used in various program logics for expressing the correctness properties and certificates.  ...  We show how to automatically infer such regular invariants of ADT-manipulating programs using finite model finders.  ...  We run CVC4 3 as a backend multi sort finite-model finder to find regular models (see Sec.3). Benchmarks.  ... 
arXiv:2108.00225v2 fatcat:skd33ohnwfhkjdrfqt2f3wyczi

Algebraic logic and logical geometry in arbitrary varieties of algebras [article]

Boris Plotkin
2012 arXiv   pre-print
It may be regarded as a brief exposition of some ideas from the book in progress: B.Plotkin, E.Aladova, E.Plotkin, "Algebraic logic and logical geometry in arbitrary varieties of algebras"  ...  The first part is devoted to logic for universal algebraic geometry. The second one deals with problems and some results.  ...  In order to do that we shall define, first, the variety of multi-sorted Halmos algebras Hal Θ . This variety Hal Θ corresponds to the initial variety of algebras Θ.  ... 
arXiv:1205.6235v2 fatcat:mdwyvq566bgundveahb7iirmmy

Multi-Sorted Residuation [chapter]

Wojciech Buszkowski
2014 Lecture Notes in Computer Science  
In section 3 we consider multi-sorted (heterogeneous) residuation algebras: abstract algebraic models of multi-sorted residuation logics.  ...  In particular, we show how multi-sorted residuated maps can be used in modal logics and linguistics.  ...  Multi-sorted logics require a multi-sorted first-order language; in particular, A ⇒ B, where A, B are of sort s, is translated into t A ≤ s t B , where t A , t B are terms of sort s which correspond to  ... 
doi:10.1007/978-3-642-54789-8_8 fatcat:53yq2bqs5jabpobjwdvnsy5ony

Bisimulation in Inquisitive Modal Logic

Ivano Ciardelli, Martin Otto
2017 Electronic Proceedings in Theoretical Computer Science  
We compare the expressiveness of InqML and first-order logic, and characterise inquisitive modal logic as the bisimulation invariant fragments of first-order logic over various classes of two-sorted relational  ...  From a model-theoretic perspective, it takes us a step in the direction of monadic second-order logic, as inquisitive modal operators involve quantification over sets of worlds.  ...  fragment of (two-sorted) first-order logic over several classes of models.  ... 
doi:10.4204/eptcs.251.11 fatcat:i3t4u5yin5empdtogcnfme5t4y

Algebraic logic and logically-geometric types in varieties of algebras [article]

Boris Plotkin, Elena Aladova, Eugene Plotkin
2011 arXiv   pre-print
We show that types appear naturally as logical kernels in the Galois correspondence between filters in the Halmos algebra of first order formulas with equalities and elementary sets in the corresponding  ...  These ties go back and forth from universal algebraic geometry to the model theory through the machinery of algebraic logic.  ...  For instance, we need multi-sorted variant of Halmos algebras in order to work with finite dimensional affine spaces and to construct geometry related to first order calculus in arbitrary Θ.  ... 
arXiv:1108.0573v1 fatcat:hwj2kcx7obdgrnzqsqhq5nazsy

Inquisitive bisimulation [article]

Ivano Ciardelli, Martin Otto
2020 arXiv   pre-print
in the sense of classical or of finite model theory.  ...  We characterise inquisitive modal logic, as well as its multi-agent epistemic S5-like variant, as the bisimulation invariant fragment of first-order logic over various natural classes of two-sorted structures  ...  This level is realised by first-order logic in a two-sorted framework that incorporates second-order objects in the second sort in a controlled fashion.  ... 
arXiv:1803.03483v2 fatcat:3zjakiealfce3pqpwciu3cwmoa

Temporal Logic in Information Systems [chapter]

Jan Chomicki, David Toman
1998 Logics for Databases and Information Systems  
In this chapter, we survey the fundamental varieties of temporal logic and describe their applications in information systems.  ...  Temporal logic is obtained by adding temporal connectives to a logic language. Explicit references to time are hidden inside the temporal connectives.  ...  First-order Temporal Logic The modal query language-first-order temporal logic-is defined to be the original single-sorted first-order logic (relational calculus) extended with a finite set of temporal  ... 
doi:10.1007/978-1-4615-5643-5_3 fatcat:bmtv3r7w2bbtfldaxefnqmsbou

Isotypeness of Models and Knowledge Bases Equivalence

Elena Aladova, Eugene Plotkin, Tatjana Plotkin
2013 Mathematics in Computer Science  
Assuming our logic to be first-order, the description of knowledge is presented by a set of first-order formulas.  ...  First of all we need a multi-sorted variant of logic, which corresponds to data and information of the different nature.  ... 
doi:10.1007/s11786-013-0166-5 fatcat:dzf3p3zcajhubinazr5fpwge5e

A Typed Hybrid Description Logic Programming Language with Polymorphic Order-Sorted DL-Typed Unification for Semantic Web Type Systems

Adrian Paschke
2007 arXiv   pre-print
term typing of LP rules based on a polymorphic, order-sorted, hybrid DL-typed unification as procedural semantics of hybrid DLPs.  ...  In this paper we elaborate on a specific application in the context of hybrid description logic programs (hybrid DLPs), namely description logic Semantic Web type systems (DL-types) which are used for  ...  In the following I describe a multi-sorted logic with a order-sorted typed unification as operational semantics which allows using external DL type systems, i.e.  ... 
arXiv:cs/0610006v2 fatcat:szfxxjpbvzej5jq6mjgbrgnmka

Knowledge bases over algebraic models. Some notes about informational equivalence [article]

Knyazhansky Marina, Plotkin Tatjana
2008 arXiv   pre-print
Further we define multi-models and automorphic equivalence of models and multi-models, that is generalization of automorphic equivalence of algebras.  ...  We also describe the concept of equivalence and formulate the criterion for the equivalence of knowledge bases defined over finite models.  ...  Knowledge Metadata (Syntax of Knowledge Representation) Knowledge metadata is described by set of formulas T using only FOL (First Order Logic).  ... 
arXiv:0807.0704v1 fatcat:xdcdfprj7bh67frrtozud6gytu

Synthesizing Inductive Lemmas for Reasoning with First-Order Logic with Least Fixpoints [article]

Adithya Murali, Lucas Peña, Eion Blanchard, Christof Löding, P. Madhusudan
2021 arXiv   pre-print
While humans divine such lemmas with intuition, we propose a technique that guides the synthesis of such lemmas using counterexamples that are finite first-order models that witness the help required for  ...  Recursively defined linked datastructures embedded in a pointer-based heap and their properties are naturally expressed in pure first-order logic with least fixpoint definitions (FO+lfp) combined with  ...  To our knowledge this is the first implementation of Natural Proofs [Löding et al. 2018; Pek et al. 2014; Qiu et al. 2013 ] that gives a general tool operating over a multi-sorted first-order logic with  ... 
arXiv:2009.10207v2 fatcat:sbg75szo5rbxxkkhxvytrukjoe
« Previous Showing results 1 — 15 out of 35,212 results