4-VL is a four-valued logic or quaternary logic.

It is based on four-valued bit code (4vbc) that names { 00, 01, 10, 11} as { not bivalent, true, false, bivalent} or { no excluded middle, true, false, excluded middle}.

This site publishes information about 4vbc for software applications, hardware implementations, and philosophical proofs.

Material to download is available and organized as follows:

For the theory of 4vbc and how it applies to the propositional, modal, and deontic logics, please see 4vbc.com; an introduction to 4vbc is located there as a pdf file;

The seminal paper is from the 8th International Conference on Boolean Problems, September 2008, in Freiberg (Sachsen), Germany, titled "Logical Foundations of Four Valued Bit Code (4VBC)", with corrigenda available on request; a paper showing that 4vbc maps Belnap-Dunn connectives OR and AND into LUTs 23 and 113 and 4vbc maps Belnap-Dunn connective IMP into LUT 77;

An executable program generating the 256 look up tables (LUTs) for the 8-bit operators in 4vbc; updated listings of LUTs sorted by LUT table number and by LUT operator bit pattern with logical symbol equivalents and existential descriptions of some of the truth tables; an explanation paper of LUT results by ranges; a paper explaining the eight new symmetrical logical operators, tentatively named with acronyms; a handy LUT for dibit operators;

Draft notes about how in quantum computing 4vbc can map the gates of C-NOT, Deutsch, Fredkin, and Toffoli; papers about multi-valued logics that show how 4vbc maps them, isolates their mistakes, and makes them incompatible with classical logic in CJ[09.8], CJ[09.9], and CJ[09.10]; a Statement of Work (SOW) for implementing 4vbc in computer hardwired devices such as a floating point gate array (FPGA);

A paper presented at the 18th International Workshop on Post-Binary ULSI Systems, May 2009, in Naha, Okinawa, Japan, titled "How to Map Software Loops and Flows into dibits of Four-Valued Bit Code", pp 42-49; a demo of the Program Correctness Verification (PCV) product that implements much of the theory in that paper, two screens for the PCV demo output, a draft PCV white paper that includes why it is immune from evil recursion; a paper about Application Program Interface Verification (APIV);

An abstract of and proof that 4vbc is a group, ring, and module; LUT results by ranges that show 4vbc does not map the F₄ multiplicative table for vector space and hence shows that table is not compatible with classical logic; a paper about how negation, rotation 1, and rotation 2 are tabular proof methods that map 4vbc LUTs as theorems; from the historical literature modal formulas not validated by PMDL; useful tetra-bit theorems in the form of quadbit LUTs;

How polyadic predicate logic maps into 8-bit code forms the basis of an abstract outline for the computational design of COMPLETE that makes use of the Polyadic Expander, Tokenizer, and Evaluator (PETE); the motivating interest is to produce an automatic and mechanically computable Universal Logic Bit Code (ULBC) for a Universal Logic System (ULS); a note on the clear mapping of inference in polyadic logic;

A draft note about bit-mistakes that is a disqualification of the proof of incompleteness of the 19 Rules of Inference by Leo Simmons (1974, 1978) in Irving M Copi (1979, 5th ed), with the same applicable to the alternate system and notation of Hilbert-Ackerman; from the same source, Why the Rule of Conditional Proof is ambiguous; a note about the unification under 4vbc of the meanings of implication in the paradox of C.I. Lewis; a disproof of the Axiom of Choice (AC) in 4vbc; a draft disproof of Strawson's first premise against free-will in 4vbc; and a rendering of deceased atheist Karl Popper's proof of the existence of God in 4vbc.

For the open standard of 4vbc, working groups, and conferences, please contact below.

For further information please write: 4-VL@cec-services.com