We present the concept of a multiple-valued logic simulator that is able to more accurately determine the possible behavior of a circuit in the presence of a bridging faults. By a user de ned mapping of a range of voltages to a logic value the simulator takes care of certain voltages more closely than common bridge fault simulators that map all voltages to either logic 1 or 0. Experimental resu...

A new logic model is presented in this paper for subsets of Ft. " x Rm known as n-input m-output r-valued multiple-valued logic (MVL) relations, where n,m > 0 and T > 1 are integers, and R = (0, 1,. .. , T-1) is an enumeration of the finite ordered set E = {eo, el,. .. , e,-1}. The model, called E2 systems (or shortly E2), represents an extension of an existing generalized cube representation f...

The polyadic algebras that arise from the algebraization of the first-order extensions of a SIC are characterized and a representation theorem is proved. Standard implicational calculi (SIC)’s were considered by H. Rasiowa [19] and include classical and intuitionistic logic and their various weakenings and fragments, the many-valued logics of Post and Lukasiewicz, modal logics that admit the ru...

As a continuation of our research work on resolutionbased automated reasoning approaches for latticevalued logic systems with truth-values in a latticevalued logical algebraic structure – lattice implication algebra (LIA), in the present paper, we prove thatα resolution for lattice-valued first-order logic ( ) LF X based on LIA can be equivalently transformed into that for lattice-valued propos...

A common standard for the interpretation of classical propositional logic is set by the functionally complete collection of 2-valued truth-tables. The structure of the free algebra of formulas is faithfully mirrored in the semantics: In each admissible model, each sentential letter freely ranges over the set of truth-values, and to each n-ary logical constant there corresponds a convenient n-ar...

We propose assertion-consistency (AC) semi-lattices as suitable orders for the analysis of partial models. Such orders express semantic entailment, multiple-viewpoint and multiple-valued analysis, maintain internal consistency of reasoning, and subsume finite De Morgan lattices. We classify those orders that are finite and distributive and apply them to design an efficient algorithm for multipl...

We develop many-valued logic, including a generic abstract model theory, over a fully abstract syntax. We show that important many-valued logic model theories, such as traditional first-order many-valued logic and fuzzy multi-algebras, may be conservatively embedded into our abstract framework. Our development is technically based upon the so-called theory of institutions of Goguen and Burstall...

The semantics of logic programs was originally described in terms of two-valued logic. Soon, however, it was realised that three-valued logic had some natural advantages, as it provides distinct values not only for truth and falsehood, but also for “undefined”. The three-valued semantics proposed by Fitting and by Kunen are closely related to what is computed by a logic program, the third truth...

In this paper we considered a moving from classical logic and Kolmogorov’s probability theory to non-classical p-adic valued logic and p-adic valued probability theory. Namely, we defined p-adic valued logic and further we constructed probability space for some ideals on truth values of p-adic valued logic. We proposed also p-adic valued inductive logic. Such a logic was considered for the firs...

After Zadeh has introduced his theory, many-valued logic began to have a new interest. Especially, Łukasiewicz logic was enclosed quite closely in fuzzy sets. There is a strong opinion that Łukasiewicz infinite-valued logic has the role as the logic of fuzzy sets, similarly as classical logic has the role as the logic of crisp sets. But actually, it seems that Kleene’s 3-valued logic was the cl...