Mechanised Uniform Interpolation for Modal Logics K, GL, and iSL

The uniform interpolation property in a given logic can be understood as the definability of propositional quantifiers. We mechanise the computation of these quantifiers and prove correctness in the Coq proof assistant for three modal logics, namely: (1) the modal logic K, for which a pen-and-paper proof exists; (2) Gödel-Löb logic GL, for which our formalisation clarifies an important point in an existing, but incomplete, sequent-style proof; and (3) intuitionistic strong Löb logic iSL, for which this is the first proof-theoretic construction of uniform interpolants. Our work also yields verified programs that allow one to compute the propositional quantifiers on any formula in this logic

Mechanised Uniform Interpolation for Modal Logics K, GL, and iSL

The uniform interpolation property in a given logic can be understood as the definability of propositional quantifiers. We mechanise the computation of these quantifiers and prove correctness in the Coq proof assistant for three modal logics, namely: (1) the modal logic K, for which a pen-and-paper proof exists; (2) Gödel-Löb logic GL, for which our formalisation clarifies an important point in an existing, but incomplete, sequent-style proof; and (3) intuitionistic strong Löb logic iSL, for which this is the first proof-theoretic construction of uniform interpolants. Our work also yields verified programs that allow one to compute the propositional quantifiers on any formula in this logic

Research in structural and solid mechanics, 1982

Advances in structural and solid mechanics, including solution procedures and the physical investigation of structural responses are discussed

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 24th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 28 regular papers presented in this volume were carefully reviewed and selected from 88 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems

Computer Aided Verification

This open access two-volume set LNCS 13371 and 13372 constitutes the refereed proceedings of the 34rd International Conference on Computer Aided Verification, CAV 2022, which was held in Haifa, Israel, in August 2022. The 40 full papers presented together with 9 tool papers and 2 case studies were carefully reviewed and selected from 209 submissions. The papers were organized in the following topical sections: Part I: Invited papers; formal methods for probabilistic programs; formal methods for neural networks; software Verification and model checking; hyperproperties and security; formal methods for hardware, cyber-physical, and hybrid systems. Part II: Probabilistic techniques; automata and logic; deductive verification and decision procedures; machine learning; synthesis and concurrency. This is an open access book

The analysis and behavior of thin-steel hyperbolic paraboloid shells

An extensive experimental and analytical investigation of thin-steel hyperbolic paraboloid (hypar) structures was carried out to provide design information. As a result of this work, empirical data is provided regarding the behavior of such structures and computer programs are presented for the analysis of thin steel hypar structures. Hyperbolic paraboloid structures possess a unique combination of structural and architectural properties, some of them are the following 1) Due to the double curvature of the surface the internal stresses in the deck are generally low and the deflections are small. 2) Since a hyper surface can be generated by straight lines, thin-steel or light-gage panels may be used to form the shell; furthermore such panels are well suited to carry the in-plane shear forces in hyper shells. 3) Basic hyper units can be combined in a large variety of ways to produce attractive roofs (Fig. 1-2, page 216). 4) The dead load to live load ratio is very low in the case of thin-steel shell structures. A hypar unit is a warped surface bounded by straight lines (Fig. I-I, page 215). The equation of the surface is z = cxy/ab. According to the simple membrane theory, a uniform load p produces pure shear forces N XY = abp/2c. This membrane shear transmits uniform eccentric axial forces to the edge members. The following are the major problems associated with the design of thin-steel hypar structures: 1) The deflections, stresses and the stability of hypars depends greatly on the shear rigidity of the thin-steel deck. This property must be evaluated experimentally for each combination of decking, connections to edge members, and seam connections. Furthermore, in the case of hypars the deck is warped and thus the shear rigidity may be different from that of an equivalent flat diaphragm. 2) The deck may buckle due to the shear stresses, and the buckling load must be evaluated for highly orthotropic shells. 3) The design of thin-steel hypar structures is generally governed by stiffness (deflections or buckling) requirements. The evaluation of the deflections is a very complex matter because it depends on the deck rigidity, the edge member axial and bending stiffnesses, and on the eccentricity of the deck-to-edge me.ber connection. 4) If the curvature (or rise-to-span ratio) of a hypar is small, the deflections may be very large and a considerable portion of the load is carried by bending nather than by membrane shear. 5) Partial or concentrated loads may cause large local deflections, especially if single-layer decks are used. The present investigation studied all the above mentioned factors. The experimental and the analytical studies are summarized briefly in the following paragraphs. The experimental investigation consisted of four types of tests: a) Four medium-scale (12 ft by 12 ft in plan) inverted umbrella tests to study the stresses, deflections, and the deck buckling, b) Test on a small-scale (2 ft by 2 ft) inverted umbrella structure to study scaling effects and the overall buckling of hypars, c) Sixteen flat shear tests to determine the shear rigidity of the decks used in the hyper tests, d) Twelve saddle-shaped hypar tests (5 ft by 5 ft in plan) with various rise-to-span ratios to evaluate the effect of rise or warping on the shear rigidity and to study other factors such as partial loading and single versus double layered decks. Photos of the various types of tests are shown in Figs. 7.1 to 7.5. The experimental program is described in detail in Chapter VII. Prior to the main test program, several small scale (2 ft by 2 ft) four-quadrant tests and medium-scale single-quadrant tests were also conducted. These tests were however discontinued because of the severe scaling effects in the case of the small-scale models and the violation of the symmetry conditions in the case of single-quadrant experiments where the neighboring quadrants were missing. Nevertheless, these tests produced useful qualitative information and experience with manuafacturing and testing thin-steel hypar structures. The edge members of the umbrella-type specimens were made of tubular members since this afforded easy connection of the warped surface to the straight edges. The decking consisted of single or double layers of standard corrugated panels. One layer was connected to the edge members with sheet metal screws at various spacings. The seam connection between the panels was also by means of sheet metal screws. In the case of shells with two layers, the top layer was connected to the bottom layer in a similar manner. The medium-scale umbrella models were loaded using air bags under each of the four quadrants. The saddle-shaped hypars were loaded with sand, whereas the small-scale models were loaded through loading pads and suspended weights. The following are the principal conclusions of the experimental part of this investigation. The effective shear stiffness of the cold-formed deck and the rise (or curvature) of the structure are the most important factors influencing the behavior of hypars. For low shear stiffnesses and for small rise-to-span ratioa the deflections may be large, the bending stresses tend to increase relative to the membrane stresses, and the possibility of deck buckling increases. As in the case of flat shear diaphragms, the shear stiffness depends strongly on the seam and edge connections. The increase in shear stiffness due to the addition of a second layer of deck was found to be only about 1/3 if the second layer was connected only to the first layer and not directly to the edge members. Similarly, the deflections of a double-layered shell are more than half of those of a corresponding single shell. If the two layers are interconnected with sheet metal screws (on an 8 in. grid in the present saddle-shaped hypar tests), the deflections are further reduced by about 10 to 20%, depending on the rise ratio. A particular problem of certain types of hypar structures is the deflection of unsupported outside corners (see Fig. 1-2, page 216). The membrane shear cannot carry the load over such flat corners and thus considerable bending and deflections may develop. The tests showed that the bending stiffness of the edge members has a great effect on the corner deflections, in fact, they indicate that the design of the edge members in hypars with flat corners is probably governed by deflection limitations. The measured bending strains in flat saddle shells (rise-to-span ratio of 1/8) was much greater than the bending in hypers with greater curvature (rise ratio of 1/3). The membrane theory is insufficient for the design of flat hypar structures. However, the design of the connections (seam or edge) may be based on the shear forces obtained from the simple membrane theory. Several single and double layered saddle-shaped models were tested under partial loading. Since such loads must be carried mainly by bending of beam strips along the deformations of single decks, relatively large deflections were noted. The deflections under the 8 in. by 8 in. loaded area were about three times greater in the single decks than on the double-layered structures. Since the effective shear rigidity of the deck is of paramount importance, the effect of curvature (warping) on it is an important question. The effective shear rigidity of various deck, edge member and connection configurations are determined by tests on flat diaphragms. The comparison of the measured deflections for saddle hypars with various rise-span ratios and the evaluation of the effective shear rigidities backwards from the measured deflections indicated that the shear rigidity is reduced by about 20% due to the warping effect. The buckling of the deck is one of the design factors. For small rise-span ratios and for low deck shear rigidities the deck may buckle. As an example, a 12 ft by 12 ft model having a single layer 24 gage corrugated sheet deck buckled at a uniform load of 70 psf (see Fig. ). This model had relatively stiff edge members (3 in. dia. tubular sections). The corner deflections remained linear with increasing load beyond the buckling load. The buckling load of double-layered structures is much larger than that for single deck shells. A model, similar to the above but with two layers of 28 gage standard corrugated decks, did not buckle up to a load of 145 psf, when the test was discontinued. The major part of the analytical investigation consisted of two finite element approaches for the calculation of deflections, stresses, and instability. In addition, two simple methods were developed for estimating the deck buckling load and the buckling of the compression edge members, which would suffice in preliminary designs. Two types of finite elements were used: curved shallow shell elements and flat elements. The details of the analysis are described in Chapter Ill. Both approaches were verified by comparisons with existing experimental and analytical results. The stiffness of the eccentric edge members were properly accounted for in the mathematical representation of the structure. The connection of the decks to the edge members may allow rotation about the axis of the edge members and movement normal to the edges due to slip at the connections. These possibilities were also considered in the analysis. The instability of the decks was studied with the help of the incremental stiffness matrix approach. The effective stiffness of the system is reduced due to the in-plane forces in the deck. The in-plane forces depend on the deflections of the shell and to obtain the buckling load, the eigenvalues of a large- order system needs to be evaluated. In the present study the load incrementation method was used instead. The effect of the in-plane forces was evaluated iteratively at successive load increments. The buckling load is obtained from the non-linear load deflection curve,(Fig. 6-6, Page 280). The comparison of the results of the flat-element and the curved-element approaches reveals that both give good results for shells supported around the perimetry. However, the flat element method gave better results in the neighborhood of unsupported flat corners. The analysis of the structures tested in this and in other studies confirmed the conclusions of the experimental part of the investigation. The stresses in most types of hypars are low and the design is usually controlled by deflection or buckling limitations. The relative stiffness of the deck and the edge members is an important factor. For stiff edge members the deck tends to bend between opposite edges, whereas in the case of flexible cantilevered edge members the shell partially supports the edge members. Analysis of a structure including the weight of the edge members indicated that this effect may have to be considered in the design of hyper structures. The analysis of buckling of hypar decks showed that the buckling load of double-layered shells is three to four times greater than that of single decks. The predicted buckling loads compared well with experimental or previous analytical evidence. The buckling load does not depend much on pre-buckling deflections, however it depends on the axial stiffness of the edge members. The finite element analysis was also used to calculate the deflection of an unsymmetrically loaded inverted umbrella structure. The results, which compared well with experimental data, showed that these deflections are about four times greater than those due to symmetric loading. This increase of deflections obviously depends on the type of structure. in this case much of the flexibility was due to the bending of the central column of the umbrella structure, Since the instability analysis of hypars by the finite element method involves considerable amount of computer capacity and expense, approximate methods were developed for the calculation of buckling loads. The buckling of the compression edge members was studied by isolating them from the structure. The instability of columns loaded by tangential axial forces that to the member remain parallel during deflection was evaluated. The results are tabulated in Fig. 6-13, page 287. The buckling of hypar decks was also investigated by the energy method (Section VI-7). The resulting equation has to be minimized to get the critical load. this can easily be done with the help of a computer. This approach is much simpler than the finite element instability analysis and is preferable in preliminary designs. A few buckling analyses of cold-formed hypar shells showed that the critical load for double-layers is about three to four times greater than a shell with a single deck

De de se

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Linguistics and Philosophy, 2006.Includes bibliographical references (p. 161-170).In this dissertation, I argue against a unitary treatment of individual de se ascription. Based on consideration of Yoruba logophors and English dream-report pronouns, I show that one mechanism is best analyzed as binding by an operator, which is sensitive to binding locality requirements. In contrast, I argue that cases of indexical shift (whereby token-reflexive elements such as I and tomorrow may be dependent on the context of an attitude predicate), which do not show local binding effects, are instances of overwriting of elements of the sequence of evaluation. As pronouns that are not obligatorily read de se show neither of the conditions for shifted indexicals nor West-African logophors, I argue that de se readings of these items must arise as special cases of de re ascription. Cross-linguistic instances of anti-logophoricity (i.e., the obligatory non-de se ascription of pronouns in certain contexts) are correspondingly treated as environments imposing a non-de se demand on de re ascription. Finally, I demonstrate that binding and overwriting mechanisms may both be found within the territory of de se long-distance anaphora, based largely on a systematic split in interpretation amongst Mandarin speakers on licensing and interpretative constraints on long-distance ziji.by Pranav Anand.Ph.D

At the intersection of temporal & modal interpretation

This work is chiefly concerned with the semantics of linguistic categories including tense, modality and negation and the relationships between them. In particular, how do they interact in order to “displace” discourse and to talk about situations remote from the time & place where they\u27re produced? What gets conventionally encoded in linguistic expressions (semantics)? And what\u27s the role of discourse context and extralinguistic factors (pragmatics) in performing these operations? The current thesis contains three connected (but independent) components; each explores different sets of data in view of understanding particular types of displacement phenomena — that is, how, in a given discourse context, reference is established to different possible worlds and different times. In other words, we are concerned with the interactions between temporal reference, modal reference and negation/polarity, and the linguistic phenomena that these give rise to. Methodologically, these projects also engage with diachronic considerations in view of explaining variation and change across spatially and temporally separate language varieties. This is motivated by the desiderata formulated by the amphichronic program --- that is, I assume that studying ostensible changes in language use over time has something to teach us about synchronic systems and vice versa, all in the service of developing an understanding of human language as a cognitive system. Each of these three component “essays” considers data from a number of languages spoken in Aboriginal Australia --- particularly Yolŋu Matha and Australian Kriol --- on the basis of both published and original data, collected on-site in the Top End in consultation with native speakers. While there is a rich tradition of Australian language description, little Australian language data has been brought to bear on the development of formal theories of meaning. Data from these languages promise to challenge and enrich the methodological and theoretical toolbox of formal semantics. Equally, it is a general contention throughout this work that formal perspectives hold exceptional promise in terms of better understanding the range of linguistic diversity exhibited across Australian languages and developing typologies of the expression of grammatical categories. ‘The emergence of apprehensionality in Australian Kriol’ considers the semantics of the adverb bambai in Australian Kriol, a creole language spoken by indigenous populations across northern Australia. Derived from English archaism by-and-by, cognates of bambai are found across contact varieties in the south Pacific. Kriol has retained the “temporal frame” use that is found in other South Pacific contact varieties (roughly `soon afterward\u27), although has also developed an identifiable “apprehensional” use. Apprehensionals, an understudied if cross-linguistically well-documented category, are taken to modalize their prejacent while implicating their speaker\u27s negative attitude vis-à-vis the possibility described in the prejacent. This essay proposes an unified analysis of the meaning contribution of bambai, analyzing the item as unambiguous and claiming that, synchronically, the apprehensional reading “emerges” reliably in discourse contexts where the truth of its prejacent is not presumed settled as a result of standard assumptions about pragmatic reasoning. Diachronically, it is shown that a similar set of processes led to the generalisation and conventionalization of bambai\u27s meaning components. ‘The semantics of the Negative Existential Cycle’ represents a semantic treatment of another little-theorized but cross-linguistically attested cyclic change as it is instantiated in a number of Australian (Pama-Nyungan) language (sub)families. The Cycle involves the recruitment of a “special” nominal negative element which diachronically displaces an older sentential negator. In this essay, the privative---a nominal case marking described in many Australian languages---is analysed as a negative quantifier. The Cycle, then, is understood as the progressive generalisation in the quantificational domain of a negative quantifier: privatives scope over nominalized event descriptions and ultimately over full sentences, at which stage they have encroached into the domain of “standard” negation. ‘Reality status & the Yolŋu verbal paradigm’ contains a description of and formal proposal for strategies of expressing temporal and modal categories in Western Dhuwal(a), a Yolŋu language of northern Arnhem Land. Crucially, this language exhibits a number of puzzling phenomena --- in particular, cyclic tense and the neutralization of reality status marking in negative sentences. As a consequence of these phenomena, the four inflectional categories that constitute WD\u27s verbal paradigm have been treated as unanalyzable from a compositional perspective. Further, neither of these phenomena has received attention in the formal semantic literature. Consequently, this essay represents the first formal proposal for the semantics WD inflectional paradigm (as instantiating a cyclic tense system and an irrealis mood which is licensed by negation) as well as the first formal analysis of these two typological phenomena