591,292 research outputs found
The converb -las in Old Tibetan
In contrast to its description in available grammars and manuals, the converb -las in Old Tibetan is used primarily to mark off the following clause as surprising given the background of the preceding clause. The converb -las enters into two distinct syntactic constructions: after a reduplicated verb it indicates the interruption of a continuous event; and in a three-clause pattern with the converb -kyis, -las introduces a surprise or contrast in the second clause, but -kyis in the third clause returns the sentiment to that of the first clause. Although the examples which demonstrate the use of -las are drawn from Old Tibetan texts, this use continues in later texts
The Choice Between Madison and FDR
This exchange is about three clauses that have often been used by the courts since the New Deal to expand federal power: the Commerce Clause, the Necessary and Proper Clause, and the Taxation Clause, from which the spending power has (at least until today) been construed. This Essay addresses the originalist interpretation of the Necessary and Proper Clause
Take-ings
The word property had many meanings in 1789, as it does today, and a critical aspect of the ongoing debate about the meaning of the Fifth Amendment\u27s Takings Clause has centered on how the word should be read in the context of the Clause. Property has been read by Professor Thomas Merrill to refer to ownership interests, by Richard Epstein in terms of a broad Blackstonian conception of the individual control of the possession, use, and disposition of resources, by Benjamin Barros as reflective of constructions through individual expectations and state law, and by the author as physical control of material possessions
As a textual matter, however, the Takings Clause is not simply concerned with governmental actions that affect property. The Clause provides that private property [shall not] be taken for public use without just compensation. It is thus concerned with property taken for public use and the word taken is the key, at least for a textualist, to understanding both which types of governmental actions fall within the ambit of the Clause and what types of property the Clause protects. The centrality of the concept of takings to the Clause\u27s meaning is reflected by the name by which the Clause is known. It is the Takings Clause, not the Property Clause. Although it has, ironically, not figured prominently in takings scholarship, the word taken is of fundamental importance to the Clause\u27s meaning. In this essay, the author explores the importance from a textualist perspective and argues that a textualist will reject the doctrine of regulatory takings
First-Order Logic Theorem Proving and Model Building via Approximation and Instantiation
In this paper we consider first-order logic theorem proving and model
building via approximation and instantiation. Given a clause set we propose its
approximation into a simplified clause set where satisfiability is decidable.
The approximation extends the signature and preserves unsatisfiability: if the
simplified clause set is satisfiable in some model, so is the original clause
set in the same model interpreted in the original signature. A refutation
generated by a decision procedure on the simplified clause set can then either
be lifted to a refutation in the original clause set, or it guides a refinement
excluding the previously found unliftable refutation. This way the approach is
refutationally complete. We do not step-wise lift refutations but conflicting
cores, finite unsatisfiable clause sets representing at least one refutation.
The approach is dual to many existing approaches in the literature because our
approximation preserves unsatisfiability
Adverbial clauses and adverbial concord
This paper speculates that the merge site of an adverbial clause, i.e. its external syntax, is determined by its derivational history, i.e. its internal syntax. Starting from the distinction between central adverbial clauses and peripheral adverbial clauses, it is first shown that the degree of integration of an adverbial clause correlates with its internal syntax, i.e. the availability of left peripheral functional material. The correlation can be informally stated as follows "the more structure is manifested in the adverbial clause, the higher it is merged". This paper develops a derivational account for this correlation. The proposal adopts the movement derivation of adverbial clauses, according to which, like relative clauses, adverbial clauses are derived by movement of a specialized IP-related operator (aspectual, temporal, modal, etc) to the left periphery. The paper explores observations drawn from the traditional literature on Japanese grammar (Minami 1974; Noda 1989; 2002) to the effect that the amount of TP-internal functional structure in an adverbial clause also correlates with the presence of specialized functional particles in the matrix clause with which the clause merges. Specifically, we explore Japanese data discussed in Endo (2011; 2012). It is proposed that the merger of an adverbial clause with the associated main clause is determined by the label of the adverbial clause, itself the result of the movement derivation
On variables with few occurrences in conjunctive normal forms
We consider the question of the existence of variables with few occurrences
in boolean conjunctive normal forms (clause-sets). Let mvd(F) for a clause-set
F denote the minimal variable-degree, the minimum of the number of occurrences
of variables. Our main result is an upper bound mvd(F) <= nM(surp(F)) <=
surp(F) + 1 + log_2(surp(F)) for lean clause-sets F in dependency on the
surplus surp(F).
- Lean clause-sets, defined as having no non-trivial autarkies, generalise
minimally unsatisfiable clause-sets.
- For the surplus we have surp(F) <= delta(F) = c(F) - n(F), using the
deficiency delta(F) of clause-sets, the difference between the number of
clauses and the number of variables.
- nM(k) is the k-th "non-Mersenne" number, skipping in the sequence of
natural numbers all numbers of the form 2^n - 1.
We conjecture that this bound is nearly precise for minimally unsatisfiable
clause-sets.
As an application of the upper bound we obtain that (arbitrary!) clause-sets
F with mvd(F) > nM(surp(F)) must have a non-trivial autarky (so clauses can be
removed satisfiability-equivalently by an assignment satisfying some clauses
and not touching the other clauses). It is open whether such an autarky can be
found in polynomial time.
As a future application we discuss the classification of minimally
unsatisfiable clause-sets depending on the deficiency.Comment: 14 pages. Revision contains more explanations, and more information
regarding the sharpness of the boun
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