Related papers: Disjunctions with stopping condition
Automated theorem provers (ATPs) can disprove conjectures by saturating a set of clauses, but the resulting saturated sets are opaque certificates. In the unit equational fragment, a saturated set can in fact be read as a convergent rewrite…
We prove that in a countable theory $T$ fully stable over a predicate $P$, any $\lam$-complete set $A$ has the $\lam$-existence property. This means that $A$ can be extended to a $\lam$-saturated model of $T$ without changing the $P$-part.…
We define the syntax and reduction relation of a recursively typed lambda calculus with a parallel case-function (a parallel conditional). The reduction is shown to be confluent. We interpret the recursive types as information systems in a…
We propose a new definition of actual cause, using structural equations to model counterfactuals. We show that the definition yields a plausible and elegant account of causation that handles well examples which have caused problems for…
This work uses mostly model-theoretic methods to establish new proof-theoretic theorems about several axiomatic theories of truth over KP (Kripke-Platek set theory) and stronger theories, especially ZF (Zermelo-Fraenkel set theory).
We propose a new definition of actual causes, using structural equations to model counterfactuals.We show that the definitions yield a plausible and elegant account ofcausation that handles well examples which have caused problems forother…
In this paper, we argue that formal systems of first order Arithmetic that admit Goedelian undecidable propositions validly are abnormally non-constructive. We argue that, in such systems, the strong representation of primitive recursive…
Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally…
Recursive saturation and resplendence are two important notions in models of arithmetic. Kaye, Kossak, and Kotlarski introduced the notion of arithmetic saturation and argued that recursive saturation might not be as rigid as first assumed.…
We prove a general decomposition theorem for the modal $\mu$-calculus $L_\mu$ in the spirit of Feferman and Vaught's theorem for disjoint unions. In particular, we show that if a structure (i.e., transition system) is composed of two…
The estimation of linear causal models (also known as structural equation models) from data is a well-known problem which has received much attention in the past. Most previous work has, however, made an explicit or implicit assumption of…
This is the report-version of a mini-series of two articles on the foundations of satisfiability of conjunctive normal forms with non-boolean variables, to appear in Fundamenta Informaticae, 2011. These two parts are here bundled in one…
Recent authors have proposed analyzing conditional reasoning through a notion of intervention on a simulation program, and have found a sound and complete axiomatization of the logic of conditionals in this setting. Here we extend this…
We apply the recently developed technology of cofinality spectrum problems to prove a range of theorems in model theory. First, we prove that any model of Peano arithmetic is $\lambda$-saturated iff it has cofinality $\geq \lambda$ and the…
We propose new definitions of (causal) explanation, using structural equations to model counterfactuals. The definition is based on the notion of actual cause, as defined and motivated in a companion paper. Essentially, an explanation is a…
Neglecting many motivating details for the Park-Pham theorem (previously known as the Kahn-Kalai conjecture), the result starts with a finite set $X$, a non-trivial upper set $\mathcal{F} \subseteq 2^X$, and a particular parameterized…
This paper first shows that the popular axiomatic systems proposed by Nute for Lewis' conditional logics are not equivalent to Lewis' original systems. In particular, the axiom CA which is derivable in Lewis' systems is not derivable in…
We consider implicit definability of the standard part {0,1,...} in nonstandard models of Peano arithmetic (PA), and we ask whether there is a model of PA in which the standard part is implicitly definable. In section 1, we define a certain…
An experiment or theory is classically explainable if it can be reproduced by some noncontextual ontological model. In this work, we adapt the notion of ontological models and generalized noncontextuality so it applies to the framework of…
We formulate a definition of the existence property that works with "structural" set theories, in the mode of ETCS (the elementary theory of the category of sets). We show that a range of structural set theories, when formulated using…