Carbon Nanotube Field Effect Transistor (CNFET) has a potential to become successor of Si-CMOS devices because of its excellent electronic properties. One of the most important challenges for the ...CNT-based technology is the undesired presence of metallic tubes which adversely impacts the performance, power and yield of CNT based circuits. Different tube configurations in CNFET transistor like Parallel Tube (PT) and Transistor Stacking (TrS) can be used to trade-off yield for performance. The Monte Carlo (MC) simulations of a full adder show that TrS implementation along with parallelism in the critical path can result in the same performance as the PT implementation (demonstrated significant improvements over CMOS) but with 4X increased functional yield and 6X reduced static power. Furthermore, we proposed architecture based on regular logic bricks that are designed using different tube configurations. Monte Carlo simulations show that for 10% metallic tubes logic bricks implemented with hybrid configurations of CNFETs can help to reduce the performance impact by 2X as compared to homogeneous bricks implemented with only TrS CNFETs. In comparison to homogeneous bricks realized with only PT CNFETs, the static power can be reduced by 2X and yield can be increased from 22% to 54%.
In the context of modal logics one standardly considers two modal operators: possibility (
◊
) and necessity (
□
) see for example Chellas (Modal logic. An introduction, Cambridge University Press, ...Cambridge, 1980). If the classical negation is present these operators can be treated as inter-definable. However, negative modalities (
◊
¬
) and (
□
¬
) are also considered in the literature see for example Béziau (Log Log Philos 15:99–111, 2006.
https://doi.org/10.12775/LLP.2006.006
); Došen (Publ L’Inst Math, Nouv Sér 35(49):3–14, 1984); Gödel, in: Feferman (ed.), Collected works, vol 1, Publications 1929–1936, Oxford University Press, New York, 1986, p. 300; Lewis and Langford (Symbolic logic, Dover Publications Inc., New York, 1959, p. 497). Both of them can be treated as negations. In Béziau (Log Log Philos 15:99–111, 2006.
https://doi.org/10.12775/LLP.2006.006
) a logic
Z
has been defined on the basis of the modal logic
S
5
.
Z
is proposed as a solution of so-called Jaśkowski’s problem see also Jaśkowski (Stud Soc Sci Torun 5:57–77, 1948). The only negation considered in the language of
Z
is ‘it is not necessary’. It appears that logic
Z
and
S
5
inter-definable. This initial correspondence result between
S
5
and
Z
has been generalised for the case of normal logics, in particular soundness-completeness results were obtained see Marcos (Log Anal 48(189–192):279–300, 2005); Mruczek-Nasieniewska and Nasieniewski (Bull Sect Log 34(4):229–248, 2005). In Mruczek-Nasieniewska and Nasieniewski (Log Univ 12:207–219, 2018.
https://doi.org/10.1007/s11787-018-0184-9
) it has been proved that there is a correspondence between
Z
-like logics and regular extensions of the smallest deontic logic. To obtain this result both negative modalities were used. This result has been strengthened in Mruczek-Nasieniewska and Nasieniewski (Bull Sect Log 46(3–4):261–280, 2017) since on the basis of classical positive logic it is enough to solely use
□
¬
to equivalently express both positive modalities and negation. Here we strengthen results given in Mruczek-Nasieniewska and Nasieniewski (Log Univ 12:207–219, 2018.
https://doi.org/10.1007/s11787-018-0184-9
) by showing correspondence for the smallest regular logic. In particular we give a syntactic formulation of a logic that corresponds to the smallest regular logic. As a result we characterise all logics that arise from regular logics. From this follows
via
respective translations a characterisation of a class of logics corresponding to some quasi-regular logics where
S
2
0
is the smallest element. Moreover, if a given quasi-regular logic is characterised by some class of models, the same class can be used to semantically characterise the logic obtained by our translation.
Interval Temporal Logic (ITL) is an established temporal formalism for
reasoning about time periods. For over 25 years, it has been applied in a
number of ways and several ITL variants, axiom systems ...and tools have been
investigated. We solve the longstanding open problem of finding a complete
axiom system for basic quantifier-free propositional ITL (PITL) with infinite
time for analysing nonterminating computational systems. Our completeness proof
uses a reduction to completeness for PITL with finite time and conventional
propositional linear-time temporal logic. Unlike completeness proofs of equally
expressive logics with nonelementary computational complexity, our semantic
approach does not use tableaux, subformula closures or explicit deductions
involving encodings of omega automata and nontrivial techniques for
complementing them. We believe that our result also provides evidence of the
naturalness of interval-based reasoning.
The paper deals with functional properties of three-valued logics. We consider the family of regular three-valued Kleene’s logics (strong, weak, intermediate) and it’s extensions by adding an ...implicative connectives (“natural” implications). The main result of our paper is the lattice that describes the relations between implicative extensions of regular logics.
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