Logics of Synonymy

We investigate synonymy in the strong sense of content identity (and not just meaning similarity). This notion is central in the philosophy of language and in applications of logic. We motivate, uniformly axiomatize, and characterize several “benchmark” notions of synonymy in the messy class of all possible notions of synonymy. This class is divided by two intuitive principles that are governed by a no-go result. We use the notion of a scenario to get a logic of synonymy (SF) which is the canonical representative of one division. In the other division, the so-called conceptivist logics, we find, e.g., the well-known system of analytic containment (AC). We axiomatize four logics of synonymy extending AC, relate them semantically and proof-theoretically to SF, and characterize them in terms of weak/strong subject matter preservation and weak/strong logical equivalence. This yields ways out of the no-go result and novel arguments—independent of a particular semantic framework—for each notion of synonymy discussed (using, e.g., Hurford disjunctions or homotopy theory). This points to pluralism about meaning and a certain non-compositionality of truth in logic programs and neural networks. And it unveils an impossibility for synonymy: if it is to preserve subject matter, then either conjunction and disjunction lose an essential property or a very weak absorption law is violated.

Reliability analysis of BiCMOS SiGe:C technology under aggressive conditions for emerging RF and mm-wave applications: proposal of reliability-aware circuit design methodology

In this contribution, the impact of extreme environmental conditions in terms of energy-level radiation of protons on silicon–germanium (SiGe)-integrated circuits is experimentally studied. Canonical representative structures including linear (passive interconnects/antennas) and non-linear (low-noise amplifiers) are used as carriers for assessing the impact of aggressive stress conditions on their performances. Perspectives for holistic modeling and characterization approaches accounting for various interaction mechanisms (substrate resistivity variations, couplings/interferences, drift in DC and radio frequency (RF) characteristics) for active samples are down to allow for optimal solutions in pushing SiGe technologies toward applications with harsh and radiation-intense environments (e.g. space, nuclear, military). Specific design prototypes are built for assessing mission-critical profiles for emerging RF and mm-wave applications.

The role of methane in projections of 21st century stratospheric water vapour

Stratospheric water vapour (SWV) is an important component of the Earth's atmosphere as it affects both radiative balance and the chemistry of the atmosphere. Key processes driving changes in SWV include dehydration of air masses transiting the cold-point tropopause (CPT) and methane oxidation. We use a chemistry–climate model to simulate changes in SWV through the 21st century following the four canonical representative concentration pathways (RCPs). Furthermore, we quantify the contribution that methane oxidation makes to SWV following each of the RCPs. Although the methane contribution to SWV maximizes in the upper stratosphere, modelled SWV trends are found to be driven predominantly by warming of the CPT rather than by increasing methane oxidation. SWV changes by −5 to 60 % (depending on the location in the atmosphere and emissions scenario) and increases in the lower stratosphere in all RCPs through the 21st century. Because the lower stratosphere is where water vapour radiative forcing maximizes, SWV's influence on surface climate is also expected to increase through the 21st century.

The role of methane in projections of 21st century stratospheric water vapour

Stratospheric water vapour (SWV) is an important component of the Earth's atmosphere as it affects both radiative balance and the chemistry of the atmosphere. Key processes driving changes in SWV through the 21st century include dehydration of air masses transiting the cold-point tropopause (CPT) and methane oxidation. Increasing surface temperatures may strengthen the Brewer-Dobson circulation, such that more methane is transported into the stratosphere where it can be oxidised to SWV. We use a chemistry-climate model to simulate changes in SWV through the 21st century following the four canonical Representative Concentration Pathways (RCPs). Furthermore, we quantify the contribution that methane oxidation makes to SWV following each of the RCPs. The methane contribution to SWV maximises in the upper stratosphere, however modelled SWV trends are found to be driven predominantly by warming of the CPT and strengthening of the Brewer-Dobson circulation rather than by increasing methane oxidation. SWV changes by −5 % to 60 % (depending on the location in the atmosphere and emissions scenario) and increases in the lower stratosphere in all RCPs through the 21st century. Because the lower stratosphere is where water vapour radiative forcing maximises, SWV's influence on surface climate is also expected to increase through the 21st century.

THE REDUCED CLIFFORD CATEGORY OF THE KACHEL SEMIGROUP ON n LETTERS

We use a new description of Kachel semigroup as triples with a pushout product. A simple Clifford category as a canonical representative (under the relation of equivalence of categories) of the standard Clifford category of this semigroup is considered.

ALMOST OVERLAP-FREE WORDS AND THE WORD PROBLEM FOR THE FREE BURNSIDE SEMIGROUP SATISFYING x2 = x3

We study the word problem for the free Burnside semigroup satisfying x2 = x3 and having two generators. The elements of this semigroup are classes of equivalent words. A natural way to solve the word problem is to select a unique "canonical" representative for each equivalence class. We prove that overlap-free words and "almost" overlap-free words can serve as canonical representatives of their equivalence classes. We show that such a word in a given class, if any, can be efficiently found. As a result, we construct a linear-time algorithm that partially solves the word problem for the semigroup under consideration.

REPRESENTATION OF SEMIAUTOMATA BY CANONICAL WORDS AND EQUIVALENCES

We study a novel representation of semiautomata, which is motivated by the method of trace-assertion specifications of software modules. Each state of the semiautomaton is represented by an arbitrary word leading to that state, the canonical word. The transitions of the semiautomaton give rise to a right congruence, the state-equivalence, on the set of input words of the semiautomaton: two words are state-equivalent if and only if they lead to the same state. We present a simple algorithm for finding a set of generators for state-equivalence. Directly from this set of generators, we construct a confluent prefix-rewriting system which permits us to transform any word to its canonical representative. In general, the rewriting system may allow infinite derivations. To address this issue, we impose the condition of prefix-continuity on the set of canonical words. A set is prefix-continuous if, whenever a word w and a prefix u of w are in the set, then all the prefixes of w longer than u are also in the set. Prefix-continuous sets include prefix-free and prefix-closed sets as special cases. We prove that the rewriting system is Noetherian if and only if the set of canonical words is prefix-continuous. Furthermore, if the set of canonical words is prefix-continuous, then the set of rewriting rules is irredundant. We show that each prefix-continuous canonical set corresponds to a spanning forest of the semiautomaton.