2,892 research outputs found
Cyclic proof systems for modal fixpoint logics
This thesis is about cyclic and ill-founded proof systems for modal fixpoint logics, with and without explicit fixpoint quantifiers.Cyclic and ill-founded proof-theory allow proofs with infinite branches or paths, as long as they satisfy some correctness conditions ensuring the validity of the conclusion. In this dissertation we design a few cyclic and ill-founded systems: a cyclic one for the weak Grzegorczyk modal logic K4Grz, based on our explanation of the phenomenon of cyclic companionship; and ill-founded and cyclic ones for the full computation tree logic CTL* and the intuitionistic linear-time temporal logic iLTL. All systems are cut-free, and the cyclic ones for K4Grz and iLTL have fully finitary correctness conditions.Lastly, we use a cyclic system for the modal mu-calculus to obtain a proof of the uniform interpolation property for the logic which differs from the original, automata-based one
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
The umbilical cord of finite model theory
Model theory was born and developed as a part of mathematical logic. It has
various application domains but is not beholden to any of them. A priori, the
research area known as finite model theory would be just a part of model theory
but didn't turn out that way. There is one application domain -- relational
database management -- that finite model theory had been beholden to during a
substantial early period when databases provided the motivation and were the
main application target for finite model theory.
Arguably, finite model theory was motivated even more by complexity theory.
But the subject of this paper is how relational database theory influenced
finite model theory.
This is NOT a scholarly history of the subject with proper credits to all
participants. My original intent was to cover just the developments that I
witnessed or participated in. The need to make the story coherent forced me to
cover some additional developments.Comment: To be published in the Logic in Computer Science column of the
February 2023 issue of the Bulletin of the European Association for
Theoretical Computer Scienc
Generic multiplicative endomorphism of a field
We introduce the model-companion of the theory of fields expanded by a unary
function for a multiplicative map, which we call ACFH. Among others, we prove
that this theory is NSOP and not simple, that the kernel of the map is a
generic pseudo-finite abelian group. We also prove that if forking satisfies
existence, then ACFH has elimination of imaginaries.Comment: 34 page
gaps as derived models and correctness of mice
Assume ZF + AD + V=L(R). Let be a gap with
admissible. We analyze as a natural form of
``derived model'' of a premouse , where is found in a generic extension
of . In particular, we will have , and if ``
exists'', then and in fact have the same universe. This
analysis will be employed in further work, yet to appear, toward a resolution
of a conjecture of Rudominer and Steel on the nature of , for
-small mice . We also establish some preliminary work toward this
conjecture in the present paper.Comment: 128 page
Which Classes of Structures are Both Pseudo-Elementary and Definable by an Infinitary Sentence
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic.When classes of structures are not first-order definable, we might still try to find a nice description. There are two common ways for doing this. One is to expand the language, leading to notions of pseudo-elementary classes, and the other is to allow infinite conjuncts and disjuncts. In this paper we examine the intersection. Namely, we address the question: Which classes of structures are both pseudo elementary and Lω1,ω-elementary? We find that these are exactly the classes that can be defined by an infinitary formula that has no infinitary disjunctions
Certificates for decision problems in temporal logic using context-based tableaux and sequent calculi.
115 p.Esta tesis trata de resolver problemas de Satisfactibilidad y Model Checking, aportando certificados del resultado. En ella, se trabaja con tres lógicas temporales: Propositional Linear Temporal Logic (PLTL), Computation Tree Logic (CTL) y Extended Computation Tree Logic (ECTL). Primero se presenta el trabajo realizado sobre Certified Satisfiability. Ahà se muestra una adaptación del ya existente método dual de tableaux y secuentes basados en contexto para satisfactibilidad de fórmulas PLTL en Negation Normal Form. Se ha trabajado la generación de certificados en el caso en el que las fórmulas son insactisfactibles. Por último, se aporta una prueba de soundness del método. Segundo, se ha optimizado con Sat Solvers el método de Certified Satisfiability para el contexto de Certified Model Checking. Se aportan varios ejemplos de sistemas y propiedades. Tercero, se ha creado un nuevo método dual de tableaux y secuentes basados en contexto para realizar Certified Satisfiability para fórmulas CTL yECTL. Se presenta el método y un algoritmo que genera tanto el modelo en el caso de que las fórmulas son satisfactibles como la prueba en el caso en que no lo sean. Por último, se presenta una implementación del método para CTL y una experimentación comparando el método propuesto con otro método de similares caracterÃsticas
Generic Stability Independence and Treeless theories
We initiate a systematic study of \emph{generic stability independence} and
introduce the class of \emph{treeless theories} in which this notion of
independence is particularly well-behaved. We show that the class of treeless
theories contains both binary theories and stable theories and give several
applications of the theory of independence for treeless theories. As a
corollary, we show that every binary NSOP theory is simple
Decidability of Difference Logic over the Reals with Uninterpreted Unary Predicates
First-order logic fragments mixing quantifiers, arithmetic, and uninterpreted
predicates are often undecidable, as is, for instance, Presburger arithmetic
extended with a single uninterpreted unary predicate. In the SMT world,
difference logic is a quite popular fragment of linear arithmetic which is less
expressive than Presburger arithmetic. Difference logic on integers with
uninterpreted unary predicates is known to be decidable, even in the presence
of quantifiers. We here show that (quantified) difference logic on real numbers
with a single uninterpreted unary predicate is undecidable, quite surprisingly.
Moreover, we prove that difference logic on integers, together with order on
reals, combined with uninterpreted unary predicates, remains decidable.Comment: This is the preprint for the submission published in CADE-29. It also
includes an additional detailed proof in the appendix. The Version of Record
of this contribution will be published in CADE-2
MAXIMALITY OF LOGIC WITHOUT IDENTITY
Lindström’s theorem obviously fails as a characterization of first-order logic without identity ( L
−
ωω
). In this note, we provide a fix: we show that L
−
ωω
is a maximal abstract logic satisfying a weak form of the isomorphism property (suitable for identity-free languages and studied in [11]), the Löwenheim–Skolem property, and compactness. Furthermore, we show that compactness can be replaced by being recursively enumerable for validity under certain conditions. In the proofs, we use a form of strong upwards Löwenheim–Skolem theorem not available in the framework with identity
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