5,057 research outputs found
Incompleteness of a first-order Gödel logic and some temporal logics of programs
It is shown that the infinite-valued first-order Gödel logic G° based on the set of truth values {1/k: k ε w {0}} U {0} is not r.e. The logic G° is the same as that obtained from the Kripke semantics for first-order intuitionistic logic with constant domains and where the order structure of the model is linear. From this, the unaxiomatizability of Kröger's temporal logic of programs (even of the fragment without the nexttime operator O) and of the authors' temporal logic of linear discrete time with gaps follows
De Jongh's Theorem for Intuitionistic Zermelo-Fraenkel Set Theory
We prove that the propositional logic of intuitionistic set theory IZF is
intuitionistic propositional logic IPC. More generally, we show that IZF has
the de Jongh property with respect to every intermediate logic that is complete
with respect to a class of finite trees. The same results follow for CZF.Comment: 12 page
On Role Logic
We present role logic, a notation for describing properties of relational
structures in shape analysis, databases, and knowledge bases. We construct role
logic using the ideas of de Bruijn's notation for lambda calculus, an encoding
of first-order logic in lambda calculus, and a simple rule for implicit
arguments of unary and binary predicates. The unrestricted version of role
logic has the expressive power of first-order logic with transitive closure.
Using a syntactic restriction on role logic formulas, we identify a natural
fragment RL^2 of role logic. We show that the RL^2 fragment has the same
expressive power as two-variable logic with counting C^2 and is therefore
decidable. We present a translation of an imperative language into the
decidable fragment RL^2, which allows compositional verification of programs
that manipulate relational structures. In addition, we show how RL^2 encodes
boolean shape analysis constraints and an expressive description logic.Comment: 20 pages. Our later SAS 2004 result builds on this wor
Towards Log-Linear Logics with Concrete Domains
We present (M denotes Markov logic networks) an
extension of the log-linear description logics -LL with
concrete domains, nominals, and instances. We use Markov logic networks (MLNs)
in order to find the most probable, classified and coherent
ontology from an knowledge base. In particular, we develop
a novel way to deal with concrete domains (also known as datatypes) by
extending MLN's cutting plane inference (CPI) algorithm.Comment: StarAI201
Inconsistency, paraconsistency and ω-inconsistency
In this paper I'll explore the relation between ω-inconsistency and plain inconsistency, in the context of theories that intend to capture semantic concepts. In particular, I'll focus on two very well known inconsistent but non-trivial theories of truth: LP and STTT. Both have the interesting feature of being able to handle semantic and arithmetic concepts, maintaining the standard model. However, it can be easily shown that both theories are ω-inconsistent. Although usually a theory of truth is generally expected to be ω-consistent, all conceptual concerns don't apply to inconsistent theories. Finally, I'll explore if it's possible to have an inconsistent, but ω-consistent theory of truth, restricting my analysis to substructural theories.Fil: Da Re, Bruno. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas; Argentina. Instituto de Investigaciones FilosĂłficas - Sadaf; Argentin
First-order Goedel logics
First-order Goedel logics are a family of infinite-valued logics where the
sets of truth values V are closed subsets of [0, 1] containing both 0 and 1.
Different such sets V in general determine different Goedel logics G_V (sets of
those formulas which evaluate to 1 in every interpretation into V). It is shown
that G_V is axiomatizable iff V is finite, V is uncountable with 0 isolated in
V, or every neighborhood of 0 in V is uncountable. Complete axiomatizations for
each of these cases are given. The r.e. prenex, negation-free, and existential
fragments of all first-order Goedel logics are also characterized.Comment: 37 page
Internal Calculi for Separation Logics
We present a general approach to axiomatise separation logics with heaplet semantics with no external features such as nominals/labels. To start with, we design the first (internal) Hilbert-style axiomatisation for the quantifier-free separation logic SL(?, -*). We instantiate the method by introducing a new separation logic with essential features: it is equipped with the separating conjunction, the predicate ls, and a natural guarded form of first-order quantification. We apply our approach for its axiomatisation. As a by-product of our method, we also establish the exact expressive power of this new logic and we show PSpace-completeness of its satisfiability problem
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