Showing papers by "Melvin Fitting published in 2018"
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TL;DR: A constant domain semantics for the first-order logic of proofs with the Barcan Formula (FOLPb) is presented; then Soundness and Completeness Theorems are proved.
Abstract: Justification logic is a term used to identify a relatively new family of modal-like logics There is an established literature about propositional justification logic, but incursions on the first-order case are scarce In this paper we present a constant domain semantics for the first-order logic of proofs with the Barcan Formula (FOLPb); then we prove Soundness and Completeness Theorems A monotonic semantics for a version of this logic without the Barcan Formula is already in the literature, but constant domains requires substantial new machinery, which may prove useful in other contexts as well Although we work mainly with one system, we also indicate how to generalize these results for the quantified version of JT45, the justification counterpart of the modal logic S5 We believe our methods are more generally applicable, but initially examining specific cases should make the work easier to follow
7 citations
01 Jan 2018
TL;DR: A basic introduction to modal logic is given, including possible world semantics, axiom systems, and quantification, and recommendations for those who want more.
Abstract: We give a basic introduction to modal logic. This includes possible world semantics, axiom systems, and quantification. Ideas and formal machinery are discussed, but all proofs (and meta-proofs) are omitted. Recommendations are given for those who want more.
5 citations
01 Jan 2018
TL;DR: The basics of tableaus and dual tableaus are examined, looking only at the most fundamental of logics, and that should be enough to make the general ideas plain.
Abstract: In a sense, tableaus and dual tableaus are the same thing, just as tableaus and sequent calculi are the same thing. There are mathematical ideas, and there are presentations of them. For applications, representing linear operators as matrices is wonderfully helpful, but for proving results about linear operators a more abstract approach is simpler and clearer. The form of mathematical structures matters psychologically for people, though perhaps it matters little to the god of mathematics who kept Paul Erdős’s book of proofs. Tableaus work towards an obvious contradiction, dual tableaus work towards an obvious truth. Which is best? Who asks the question? That determines the answer. Here we examine the basics of tableaus and dual tableaus and their connections, looking only at the most fundamental of logics. That should be enough to make the general ideas plain.