Related papers: Continuous logic and the strict order property
Although randomization has long been used in distributed computing, formal methods for reasoning about probabilistic concurrent programs have lagged behind. No existing program logics can express specifications about the full distributions…
This paper discusses system consequence, a central idea in the project to lift the theory of information flow to the abstract level of universal logic and the theory of institutions. The theory of information flow is a theory of distributed…
In this note we collect several observations on state extensions. They may be instrumental to anyone who pursues the theory of quantum logics. In particular, we find out when extensions (resp. signed extensions) exist in the "concrete"…
We provide a general and syntactically-defined family of sequent calculi, called \emph{semi-analytic}, to formalize the informal notion of a "nice" sequent calculus. We show that any sufficiently strong (multimodal) substructural logic with…
A concept of "guessability" is defined for sets of sequences of naturals. Eventually, these sets are thoroughly characterized. To do this, a nonstandard logic is developed, a logic containing symbols for the ellipsis as well as for…
We demonstrate that any $\Pi_\alpha$ sentence of the infinitary logic $L_{\omega_1 \omega}$ extending the theory of linear orderings has a model with a $\Pi_{\alpha+4}$ Scott sentence and hence of Scott rank at most $\alpha+3$. In other…
Matatyahu Rubin has shown that a sharp version of Vaught's conjecture, $I({\mathcal T},\omega )\in \{ 0,1,{\mathfrak{c}}\}$, holds for each complete theory of linear order ${\mathcal T}$. We show that the same is true for each complete…
In process algebras such as ACP (Algebra of Communicating Processes), parallel processes are considered to be interleaved in an arbitrary way. In the case of multi-threading as found in contemporary programming languages, parallel processes…
Every countable language which conforms to classical logic is shown to have an extension which conforms to classical logic, and has a definitional theory of truth. That extension has a semantical theory of truth, if every sentence of the…
We study semi-isolation as a binary relation on the locus of a complete type and prove that under some additional assumptions it induces the strict order property.
Consistency properties of concurrent computations, e.g., sequential consistency, linearizability, or eventual consistency, are essential for devising correct concurrent algorithms. In this paper, we present a logical formalization of such…
In this paper, we elaborate ring theoretic properties of nodal orders. In particular, we prove that they are closed under taking crossed products with finite groups.
Distributive laws are important for algebraic reasoning in arithmetic and logic. They are equally important for algebraic reasoning about concurrent programs. In existing theories such as Concurrent Kleene Algebra, only partial correctness…
For many standard models of random structure, first-order logic sentences exhibit a convergence phenomenon on random inputs. The most well-known example is for random graphs with constant edge probability, where the probabilities of…
We propose a generalization of first-order logic originating in a neglected work by C.C. Chang: a natural and generic correspondence language for any types of structures which can be recast as Set-coalgebras. We discuss axiomatization and…
Sequential hypothesis testing asks for decision rules that update as data arrive. A natural goal is \emph{eventual correctness}: the rule may change its mind early on, but it should make only finitely many wrong decisions almost surely.…
We define the continuous modeling property for first-order structures and show that a first-order structure has the continuous modelling property if and only if its age has the embedding Ramsey property. We use generalized indiscernible…
Abstract. Matching logic cannot handle concurrency. We introduce concurrent matching logic (CML) to reason about fault-free partial correctness of shared-memory concurrent programs. We also present a soundness proof for concurrent matching…
Interest prohibition theory concerns theoretical aspects of interest prohibition. We attempt to lay down some aspects of interest prohibition theory wrapped in a larger framework of informal logic. The reason for this is that interest…
Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a semantical platform and research program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth which it has more…