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LC Type Logic

Research into Type-Logical semantics and its application to real world problems of inference and knowledge management has been conducted over the past three decades by Erik Thomsen, one of DSSlab's founding team members. That research led to a new paradigm for logic - one based on cognitive processing (i.e., where process is central to logic, and 'logic' is taken in its traditional sense to include language and mathematics). And to a new model within that paradigm.

Here below, under 2012, you will find an articulation of the of the cognitive processing paradigm and a formal exposition of the new model for logic. Following that is a chronological introduction to that research highlighting major research questions per time period and with links to relevant papers and patents. Many of the papers were written during the print era. They are currently being digitized.

2012: Draft form of a new paradigm and a formal model for logic

Why you should read this book

Short teasers for logicians, philosophers of language, computational linguists and mathematicians

How the Great War impacted the roots of modern logic

An historical introduction to the unfinished research program of Bertrand Russell and Ludwig Wittgenstein and why it is relevant today

A Critique of the consensus paradigm in logic

An introduction to the consensus paradigm and a detailed description of its most cripling flaws

A new paradigm for logic

Describes cognition and awareness through a collection of multiple levels of embedded processes. Points the way to a new view of the mind-body distinction. And a new grounding for logic.

Knowing the World is Language

A theory of logic based on a new paradigm of cognitive processing that also provides a foundation for language and mathematics

2007-2011: start ups and consulting: prototyping specific type engine-based applications

Research questions
� How to extract the dimensional model implicit within a collection of spreadsheets
� How to generate image signatures without the use of pre-defined ontologies in a way that would make them comprehensible to humans
� How to extract testable propositions from text
� How to parse text into a logical form that immediately integrates with a knowlege store
� How to represent disparate information in a semantically unified fashion
�How to infer across quantitative and qualitative information in the presence of uncertainties, and inconsistencies

Papers/output
� Overview to the LC Logical Typing System
� LC Foundations of Abstract Science
� Logical implication for propositional variables in LC Type Logic
� Logical implication for predicate variables in LC Type logic
� Patent filing (#20100169758) Extracting Semantics from Data
� A critique of the consensus paradigm in logic

2003-2007: Working for a large corporation building Type Engine pieces and applications for business

Research questions

� Computational models for organizational performance management
� Abstract definitional layers that support federated heterogeneous query processing
� Next gen Type Engines

Papers/output

� Organizational performance management: grounding papers
� Enterprise risk management
� Patent (#7,797,320) on a method for computing semi-orthogonal partial bases in N dimensional categorical data sets
� Patent (#7,631,005) on a method for defining nested irregular views

1994-2003 Period of application and synthesis

Research questions
� What are the core theoretical problems with canonical logic?
� What are the core theoretical problems with canonical mathematics
� How do the foundations of math and logic relate to software?
o Theoretical aspects
o Applied aspects
� First cut of a foundation for abstract science
� What are the key functional characteristics of Type Engines as compared with current Relational or Multidimensional database architectures

Papers/output
� Relating LC to the Canonical foundations of Mathematics
� Relating LC to Canonical Logic
� Overview of the relation between LC and Canonical Logic
� OLAP Solutions 2nd edition
� Microsoft OLAP Solutions
� OLAP Solutions 1st edition
� Synthesizing knowledge from large data sets

1988-1994: First cut at an alternative foundation, first cut at mapping it to canonical beliefs/approaches, first application to software

Research questions:
� What is the core process of meaning creation?
� What foundational problems (aka paradoxes) does this process/approach resolve?
� What practical problems can be solved by software that follows this approach?

Papers/output

� Kirkberg Austria 1993: Foundations of Logic

Peer-reviewed paper
"Subsuming multi valued logics in a two tiered bi-valent approach"
presented at the Wittgenstein Symposium on the Foundations of Logic
Austria 1993;

� Kirkberg Austria 1992: Foundations of Mathematics

Peer-reviewed paper and publication
"A Functional Basis for Tractarian Number Theory"
presented at the Wittgenstein Symposium on the Foundations of Mathematics
Austria 1992; published in Wittgenstein's Philosophy of Mathematics
Verlag Holder-Pichler-Tempsky Wien 1993

� Kirkberg Austria 1989: Foundations of Language

Peer-reviewed paper and publication
"A Tractarian Approach to Information Modeling"
presented at the Wittgenstein Symposium on the Foundations of Language
Austria 1989; published in Wittgenstein-Towards a Re-evaluation
Verlag Holder-Pichler-Tempsky Wien 1990

� FreeThink (user manual and docs)

1982 - 1988: Foundational research

Research Questions
� What are the criteria for meaningfulness as relates to any kind of expression?
� What is the smallest number of most irreducible dimensions that can be used to relate any expression with any expression?
� How do these criteria for meaningfulness map to those of LW in the Tractatus?

Papers/output:
� Adding to Space and Time 1988
� Relating Axiomatic systems to Empirical Knowledge
� Patent for multi level hierarchies

The story that connects the research questions to the papers
My research journey began in 1982 while working on a thesis that attempted to unify the variety of approaches to Economics including Macro and Micro, Communism and Capitalism, and Buddhist and Western, with an emphasis on growth theory. That's when I discovered that the multi-level mixed empirical/definitional mathematics I was assuming existed to help me "prove" the theory did not in fact exist.

So I left school (with the tacit support of two of my thesis advisors) to pursue the mathematics. During this time numerous themes and ideas kept reoccurring:
� The stuff that gets exchanged, (i.e., the symbols) should not be confused with the things doing the exchanging, (i.e., the cognitive processing entities)
� Analog needs to marry with symbolic
� Sensory-motor needs to marry with symbolic language
� Language, Logic and Mathematics seem to be different views into the same underlying substrate
� Language primitives should Not go proxy for the world nor bear any referentially defined ontological commitments
� Boy is there a lot of scale or granularity complexity in the world that needs more formal methods of representation

Though they all kept popping up, this last one, the scale one was ubiquitous. It's formalization was a precondition for the others.

This precipitated the "Adding to Space and Time" paper written in 1987/88. The purpose of the paper was to demonstrate that "time" and "space" were incomplete as a characterization of general/universal topology -both in the physics sense and the language sense of the term "topology". The concept of scale, missing as an intrinsic part of both time and space, (clearly present in physics but not fully baked in) was not simply added as a third kind of dimension. Rather it was shown that what we think of as ruler-like space and clock-like time are more accurately described as space-position and time-position respectively. And that it is only possible to measure position if scale is known (and typically assumed constant) during the act of measurement. And that scale pops up as space-scale and time-scale (again, measured for a given position). Moreover, "time" and "space" are best thought of as opposite binary values in the same way as position and scale. Topology itself thereby followed from the cross product of two binary distinctions.

The paper had been written with the intent to be submitted for publication in Mind magazine. Every article written during the 20th century on the topic that was published in Mind as well as everything else I could find was discussed in the article. However, I wound up co-founding a software company at the same time and the ideas in the article were embedded in both our flagship software product - FreeThink- and in a patent that took 5 years to file but which was one of the defining patents of the BI software industry and which covered the core dimensional technology in what later became known as the multidimensional database industry.