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Elements of model theory
Published in Uri Abraham, Models for Concurrency, 2020
Next formulas are defined; first atomic and then compound formulas. An atomic formula is any sequence of symbols of the form P(τ1,…, τn) where P is a predicate of arity n and each τi is a term of the appropriate sort (which sorts can be in the ith coordinate is determined by sort(P)). The equality predicate = exists in every signature (but the tradition is to write τ1 = τ2 rather than = (τ1,τ2)).
Order and Logic
Published in Pascal Hitzler, Anthony Seda, Mathematical Aspects of Logic Programming Semantics, 2016
1.2.2 Definition An atom, atomic formula, or proposition A (over A) is an expression of the form p(t1, ... , tn), where p is an n-ary predicate symbol in A and t1, ... , tn are terms (over A).
Doxastic logic: a new approach
Published in Journal of Applied Non-Classical Logics, 2018
I will use the following language, , in this paper: Any constant or variable is a term.If are any terms and P is any n-place predicate, is an atomic formula.If t is a term, Et (‘t exists’) is an atomic formula and Rt (‘t is perfectly rational [reasonable, wise]’) is an atomic formula.If s and t are terms, then s=t (‘s is identical with t’) is an atomic formula.If A and B are formulas, so are , , , and .If A is a formula, so are (‘it is universally [or absolutely] necessary that A’), (‘it is universally [or absolutely] possible that A’), (‘it is [relatively] necessary that A’) and (‘it is [relatively] possible that A’).If A is any formula and t is any term, then (‘t believes that [it is the case that] A’) and (‘it is doxastically conceivable for t that A’) are formulas.If A is any formula and x is any variable, then (‘for every [possible] x: A’) and (‘for some [possible] x: A’) are formulas.Nothing else is a formula.