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

2016
*
arXiv
*
pre-print

This work extends the existing MACE-style

arXiv:1604.08040v1
fatcat:3mwe45k45fb5lefbu53sfouupi
*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. ...##
###
Expressive power and abstraction in Essence

2008
*
Constraints
*

Development of languages for specifying or

doi:10.1007/s10601-008-9050-3
fatcat:dg64v3pux5gs5pxxxljiqgwl5y
*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 . ...##
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Non-cyclic Sorts for First-Order Satisfiability
[chapter]

2013
*
Lecture Notes in Computer Science
*

We implemented our

doi:10.1007/978-3-642-40885-4_15
fatcat:qrsnrwxiuzbfpn3hwjvydmuhgq
*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] . ...##
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ALGEBRAIC LOGIC AND LOGICALLY-GEOMETRIC TYPES IN VARIETIES OF ALGEBRAS

2013
*
Journal of Algebra and its Applications
*

We show that types appear naturally as

doi:10.1142/s0219498812501460
fatcat:w2g2zehnobd6zl4mtwyg3n7zgi
*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. ...##
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Solving Constrained Horn Clauses over ADTs by Finite Model Finding
[article]

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. ...

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

2012
*
arXiv
*
pre-print

It may be regarded as a brief exposition of some ideas from the book

arXiv:1205.6235v2
fatcat:mdwyvq566bgundveahb7iirmmy
*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. ...##
###
Multi-Sorted Residuation
[chapter]

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 ...

##
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Bisimulation in Inquisitive Modal Logic

2017
*
Electronic Proceedings in Theoretical Computer Science
*

We compare the expressiveness of InqML and

doi:10.4204/eptcs.251.11
fatcat:i3t4u5yin5empdtogcnfme5t4y
*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*. ...##
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Algebraic logic and logically-geometric types in varieties of algebras
[article]

2011
*
arXiv
*
pre-print

We show that types appear naturally as

arXiv:1108.0573v1
fatcat:hwj2kcx7obdgrnzqsqhq5nazsy
*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. ...##
###
Inquisitive bisimulation
[article]

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. ...

##
###
Temporal Logic in Information Systems
[chapter]

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 ...

##
###
Isotypeness of Models and Knowledge Bases Equivalence

2013
*
Mathematics in Computer Science
*

Assuming our

doi:10.1007/s11786-013-0166-5
fatcat:dzf3p3zcajhubinazr5fpwge5e
*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. ...##
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A Typed Hybrid Description Logic Programming Language with Polymorphic Order-Sorted DL-Typed Unification for Semantic Web Type Systems

2007
*
arXiv
*
pre-print

term typing of LP rules based on a polymorphic,

arXiv:cs/0610006v2
fatcat:szfxxjpbvzej5jq6mjgbrgnmka
*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. ...##
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Knowledge bases over algebraic models. Some notes about informational equivalence
[article]

2008
*
arXiv
*
pre-print

Further we define

arXiv:0807.0704v1
fatcat:xdcdfprj7bh67frrtozud6gytu
*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*). ...##
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Synthesizing Inductive Lemmas for Reasoning with First-Order Logic with Least Fixpoints
[article]

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

arXiv:2009.10207v2
fatcat:sbg75szo5rbxxkkhxvytrukjoe
*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 ...
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