Also to clarify, my thesis discusses use of natural language in support of various forms of reasoning and learning. Chapter 3 discusses how the thesis approach could support deduction, induction, abduction, analogical reasoning, causal and purposive reasoning, learning by multi-level reasoning, reflection, invention of languages, curiosity, imagination, etc.
I agree broadly with the statements by John Sowa and Pat Hayes, about the value of natural language, and the value of formal logic - indeed, the thesis directly quotes John regarding this, in section 3.2.1. The thesis approach permits both, but does not require translating natural language into formal logic.
To avoid over-simplifying, will just encourage people who are interested to read the thesis, perhaps starting with the slides.
(links included for readers who may be new to the thread.)
Date: Wed, 25 Jun 2014 17:22:00 -0400
Subject: Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology
You included analogy reasoning twice. I didn't see you mention abductive reasoning.
Most people also specifically list deductive reasoning.
I notice you forgot that FOL also includes negation.
FOL and Common Logic (a superset of FOL)
both have quantifiers ForAll and ThereExists
over its Universe of Discourse.
FOL does NOT include relations & functions
in its Universe of Discourse, Common Logic does.
A lot of people differentiate modal logic, situation logic
and temporal logic.
The basic unary (1-place) modal operators are commonly
written □ (square box) for Necessarily and ◇ (diamond)
for Possibly and ~ (tilde) for negation.
I haven't seen any specific notation for situation logic or
temporal logic. It may exist, but I haven't seen it commonly
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