Statemental credibility logic for intelligent systems

Statemental algebra and truth calculus for unmanned systems

“…In a recent paper of ours [3], we analyzed the operations involved in different types of statements, including dichotomy, fuzzy, probabilistic, and probabilistic fuzzy, as demonstrated below. (i) A dichotomy statement is a declarative sentence which is either true or false, also known as a proposition.…”

“…There is no consensus on what constitutes absolute truth and falsehood. To tackle this ultimate philosophical problem, we introduced benchmarks of truth and falsehood as a practical alternative to absolute truth and falsehood in our previous paper [3]. We propose that a statement can serve as the benchmark of truth if it is so strongly supported by fact or reality that no one doubts it.…”

“…Throughout this paper, we will denote the benchmark of truth by ⊤ and the benchmark of falsehood by ⊥. In our previous paper [3], we presented a method for symbolically representing the operations of statements. Specifically, we considered three types of statemental operations:…”

“…In our earlier paper [3], we used the aforementioned self-evident laws of natural language as axioms to develop an algebra of statements. The axiomization requires the use of the following general concept of an equivalence relation.…”

“…In this subsection, we will provide specific rules for making deductions within a statemental algebra (S , ∧, ∨, ¬, ≡, ⊥, ⊤), even when dealing with vague or random statements. All of the rules that we present can be proven using Theorem 19 or the general deduction principle that was introduced in our paper [4], through the use of truth tables. While our deduction rules resemble those in propositional calculus, there is a key conceptual difference: our rules apply to all types of statements, including dichotomy, probabilistic, fuzzy, and probabilistic fuzzy types.…”