In his well-known paper \How computer should think" ((Be77b]) Belnap argues that four valued semantics is a very suitable setting for computerized reasoning. In this paper we vindicate this thesis by showing that the logical role that the four-valued structure has among Ginsberg's well-known bilattices is similar to the role that the two-valued algebra has among Boolean algebras. Speciically, w...

We obtain, for the first time, a modular many-valued semantics combined logics, which is built directly from logics being combined, by means of suitable universal operations over partial non-deterministic logical matrices. Our constructions preserve finite-valuedness in context multiple-conclusion whereas, unsurprisingly, it may be lost single-conclusion logics. Besides illustrating our wide ra...

In recent years, interest in many-valued logics for computer science has increased considerably, and there is certainly a need for good and thorough textbooks on the subject geared towards that potential area of application, namely, computer science. The authors of the volume Many-valued Logics 1 , Leonard Bolc and Piotr Borowik, have set out to do just that. The volume under review here is the...

The inference rule !-resolution was introduced in [27] as a technique for developing an SLD-style query answering procedure for the logic programming subset of annotated logic. The inference rule requires that the lattice of truth values be ordinary. In this paper, it is proved that all complete distributive lattices are ordinary. Properties of !-resolution in the general theorem proving settin...

Several interpretations can be given to the third truth value in three-valued logics. Here, we consider the case when it refers to the epistemic notion of contradictory, or both true and false at the same time. We study several paraconsistent threevalued logics that carry this concern and show that they can be translated into a fragment of a simple epistemic logic where modalities can only appe...

This paper obtains an effective method which assigns two-valued semantics to every finite-valued truth-functional logic (in the direction of the so-called “Suszko’s Thesis”), provided that its truth-values can be individualized by means of its linguistic resources. Such two-valued semantics permit us to obtain new tableau proof systems for a wide class of finitevalued logics, including the main...

In this paper the design of a new high-speed current mode BiCMOS logic circuits isproposed. By altering the threshold detector circuit of the conventional current mode logic circuitsand applying the multiple value logic (MVL) approach the number of transistors in basic logicoperators are significantly reduced and hence a reduction of chip area and power dissipation as wellas an increase in spee...

Multi-valued logics support the explicit modeling of uncertainty and disagreement by allowing additional truth values in the logic. Such logics can be used for verification of dynamic properties of systems where complete, agreed upon models of the system are not available. In this paper, we present an implementation of a symbolic model checker for multi-valued temporal logics. The model checker...

While the purpose of a conventional proof calculus is to axiomatise the set of valid sentences of a given logic, a refutation system, or complementary calculus, is concerned with axiomatising the invalid sentences. Instead of exhaustively searching for counter models for some sentence, refutation systems establish invalidity by deduction and thus in a purely syntactic way. Such systems are rele...

A well-known result by Wójcicki-Lindenbaum shows that any tarskian logic is many-valued, and another result by Suszko shows how to provide 2-valued semantics to these very same logics. This paper investigates the question of obtaining 2-valued semantics for many-valued logics, including paraconsistent logics, in the lines of the so-called “Suszko’s Thesis”. We set up the bases for developing a ...