A part of relativistic dynamics (or mechanics) is axiomatized by simple and purely geometrical axioms formulated within first-order logic. A geometrical proof of the formula connecting relativistic and rest masses of bodies is presented, leading up to a geometric explanation of Einstein’s famous E = mc. The connection of our geometrical axioms and the usual axioms on the conservation of mass, m...

We present a streamlined axiom system of special relativity in first-order logic. From this axiom system we “derive” an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform into those of general relativity. This way we hope to make general relativity more accessible for the non-specialist.

The purpose of this note is to acknowledge a gap in a previous paper — “The Complexity of Revision”, see [1] — and provide a corrected version of argument. The gap was originally pointed out by Francesco Orilia (personal communication and [4]), and the fix was developed in correspondence with Vann McGee. The main point of the argument given in [1] is to show that the Gupta-Belnap revision-theor...

We show how Leibnitz.s indiscernibility principle and Gentzen's original work lead to extensions of the sequent calculus to first order logic with equality and investigate the cut elimination property. Furthermore we discuss and improve the nonlengthening property of Lifshitz and Orevkov.

We present a new inference system for first-order logic, SIGRes, which couples together SInst-Gen and ordered resolution into a single inference system. Given a set F of first order clauses we create two sets, P and R, each a subset of F . Under SIG-Res, P is saturated by SInst-Gen and resolution is applied to pairs of clauses in P ∪R where at least one of the clauses is in R. We discuss the mo...

Abstract. The probability of a property on the collection of all finite relational structures is the limit as n ! 1 of the fraction of structures with n elements satisfying the property, provided the limit exists. It is known that the 0-1 law holds for every property expressible in first-order logic, i.e., the probability of every such property exists and is either 0 or 1. Moreover, the associa...

We examine one consequence for the generic theory TC of a geometric Fraïssé C when C has the 0,1-law for first-order logic with convergence to TC itself. We show that in this scenario, if the asymptotic probability measure in play is not terribly exotic, then C is “very close” to being a 1-dimensional asymptotic class – so that TC is super-simple of finite SU -rank.

A first-order theory has the Schröder-Bernstein Property if any two of its models that are elementarily bi-embeddable are isomorphic. We prove (as Theorem 3.8): Theorem 1. If G is an abelian group, then the following are equivalent: 1. Th(G,+) has the Schröder-Bernstein property; 2. Th(G,+) is ω-stable; 3. G is the direct sum of a divisible group and a torsion group of

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Possibilistic logic is a logic of uncertainty tailored for reasoning under incomplete evidence and partially inconsistent knowledge. At the syntactic level it handles formulas of propositional or first-order logic to which are attached numbers between 0 and 1, or more generally elements in a totally ordered set. These weights are lower bounds on so-called degrees of necessity or degrees of poss...