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<p> A core technique of modern tools for formally reasoning about computing systems is generating and dispatching queries to automated theorem provers, including Satisfiability Modulo Theories (SMT) provers. SMT provers aim at the tight integration of decision procedures for propositional satisfiability and decision procedures for fixed first-order theories &ndash; known as theory solvers. This thesis presents several advancements in the design and implementation of theory solvers for quantifier-free linear real, integer, and mixed integer and real arithmetic. These are implemented within the SMT system CVC4. We begin by formally describing the Satisfiability Modulo Theories problem and the role of theory solvers within CVC4. We discuss known techniques for building solvers for quantifier-free linear real, integer, and mixed integer and real arithmetic around the Simplex for SMT algorithm. We give several small improvements to theory solvers using this algorithm and describe the implementation and theory of this algorithm in detail. To extend the class of problems that the theory solver can robustly support, we borrow and adapt several techniques from linear programming (LP) and mixed integer programming (MIP) solvers which come from the tradition of optimization. We propose a new decision procedure for quantifier-free linear real arithmetic that replaces the Simplex for SMT algorithm with a variant of the Simplex algorithm that performs a form of optimization &ndash; minimizing the sum of infeasibilties. In this thesis, we additionally describe techniques for leveraging LP and MIP solvers to improve the performance of SMT solvers without compromising correctness. Previous efforts to leverage such solvers in the context of SMT have concluded that in addition to being potentially unsound, such solvers are too heavyweight to compete in the context of SMT. We present an empirical comparison against other state-of-the-art SMT tools to demonstrate the effectiveness of the proposed solutions.</p>

This work is in three parts. The first considers the most popular symbolic approach to the modalities and finds crucial shortcomings in it. The second explores the nature of symbolization and of logical form, and the third, drawing on the conclusions of the first two, sketches a symbolic treatment appropriate for certain types of talk about "necessity". The systems considered in Part 1 are those of C. I. Lewis and his followers. It is argued that they are unsuitable for use in symbolizing everyday modal talk, (i) because they do not have constants such as we should need for representing particular modalized utterances, and (ii) because they represent the valuation applied to those utterances which can be symbolized as being dependent upon features of symbolic systems rather than upon features of the symbolizanda. In Part 2 attention is focussed on various levels of symbolization, ranging from the symbolic use of a knot in one's handkerchief to the construction of a fully-fledged logical calculus complete with a truth-table formulation. Further the nature of logical form is explored, and it is concluded from these two investigations that the first step in symbolizing any new subject matter should be to seek out some range of valuations applicable to, and interesting for, that subject matter. The final part considers what is involved in claiming that something is necessary - whether in an everyday or a scientific context - and what it is for such a claim to "be "acceptable". It is argued that many - and probably the most important - uses of the term "necessary" are in utterances which should be symbolized as ad hoc postulates prefixed to normal truth-functional calculus symbolizations This application of the approach argued for in Part 2 is complemented by some notes on other approaches to necessity and possibility, and the discussion is rounded off with the suggestion that further application of the "valuational" approach offers the best prospect for substantial advances in modal logic. Part 1 In Symbolic Logic Lewis sets out to show that his connective '→' is superior to the '⊃' of the truth-functional prepositional calculus ('KC'). The superiority lies in the fact that for a "particular p and q" 'p → q' holds if and only if q is deducible from p; that is, Lewis claims, if 'p⊃q'is a tautology. It is unclear whether 'p' and 'q' are constants or variables. They are spoken of as "particular" and equated with individual utterances, yet they are, as arguments of a tautologous formula, presumably variables of KC. Further, the aspects of arguments of '→' which determine whether the relationship holds are the particular structures of these arguments and not the particular valuations assignable to simple variables of Lewis's system. The attempt to specify the conditions under which a formula consisting of two constant expressions bound by '→' should be assigned a true utterance as interpretation leads to a bizarre conclusion even when allowance is made for- Lewis's personal view of tautologousness and for various readings of his argument. The matter is to be decided, it seems, only by taking utterances such as would be symbolized by the two arguments of '→', symbolizing these utterances in some other calculus (presumably KC) and deciding whether the generalization of the resulting formula is a tautology. Lewis's aims and methods are the root of the troubles. Although he condemns KC as unable to represent deducibility properly, he wishes his system to contain KC. This he hopes to achieve by retaining the existing apparatus of KC, adding a new operator and, inevitably, accepting the lack of any finite general method for determining the value of a formula. Were this new operator to have had any influence upon what can be proved, then the individual symbols of the resulting system would have ceased to be comparable to KC symbols; for to choose a KC symbol as a means of representing an utterance is to accept that all and only its truth-functional relationships are worth symbolizing, but to choose the other sort of symbol would be to take more or different relationships as important-with the result that a quite different structure might turn out to give the most suitable representation of the utterance concerned. In KC there is a simple general rule laying down what value is assigned to the formula composed of a material implication sign and two constants of given value. It is our knowledge of such rules which allows us to decide that KC is a suitable calculus for a given application. We are able to see that when we use designated constants to symbolize (all and only) true utterances, the fact that a given material implication is a designated formula has a certain significance. The lack of such a general rule makes it a step in the dark if we decide to apply the Lewis.systems and take designated constants to symbolize the true utterances we are considering. Furthermore it is clear that in order to assure ourselves of a strict implication holding for a given pair of expressions, we must complicate the structure of our symbolizations of them until the corresponding material implication, regarded as a KC formula, instantiates some theorem; or else we must introduce the desired strict implication directly as a designated (constant) formula. Since one is forced to introduce those strict implications which one wishes to employ later, as a deliberate part of the choice of symbolization for the individual utterances to which the system is to be applied, the symbol '→' may be seen as little more than a deviantly manipulated predicate, or 'P → Q' may be seen as a single constant whose use is restricted to cases where 'P' and 'Q' occur separately in such a way that 'P⊃Q' is designated. One may thus agree with Lewis's comment that "the only case in which any truth-implication is likely to have any value in application, as the basis of inference, is the case in which it coincides with strict implication." The most satisfactory view of his system is as -a meta-logic designed to deal with deducibility-relations within KC, and itself behaving as a truth-functional predicate calculus but lacking any distinction between variables of the meta- logic and variables of the object-logic, (that is, the 'p's and 'q's making up "particular" KC formulae dealt with). A consideration of several writers who have attempted to extend and interpret Lewis systems- reveals neither a solution to the problem of the nature of their constants, nor recognition of the philosophical significance of the absence of any finite general truth-table treatment for '→'. This in no way depreciates the mathematical and logical ingenuity with which models for Lewis systems have been devised, but does leave the question of how the modalities should be symbolized a much more open one than might have been supposed. The question is best approached by considering what is involved in symbolizing a particular subject matter and what one should expect from a successful symbolization. Part 2 In examining various levels of symbolic apparatus and the criteria for preferring one system to another at each level, we are led to the conclusion that logical symbolization should always be seen as relative to some "valuation" of the symbolizanda, and that when given the task of constructing a logic for something one should begin by seeking the most interesting and important valuations applicable to it. It is further argued that logical form can only be determined in the light of knowing in which calculus and to which depth it is intended to conduct the symbolization.

This thesis investigates the prospects for an interpretivist account of practical reasons. The proposed account identifies practical reasons with sets of propositional attitudes from which certain actions follow, given the constraints of interpretable functioning. Following Davidson, these constraints are taken to be enumerated by formal decision theory and formal semantics. Thus the account of practical reasons is framed in terms of what rationally follows from agents' beliefs and desires. The hope is that an account of practical reasons of this kind can explain the existence of practical reasons without invoking irreducible normative properties or relations. This outcome depends upon the availability of a theory of (radical) interpretation which is free from prior normative commitments. It is argued that a non-normative reading of Davidson's theory of radical interpretation is available, such that the account of practical reasons can meet this requirement. Although the proposed account of practical reasons does not admit of the possibility of categorical reasons for action, the ensuing objection that it fails to allow for the possibility of moral reasons for action is resisted. It is suggested that a plausible account on which moral reasons are hypothetical in kind can be provided. In particular, an account of moral reasons which is framed in terms of the motivations associated with a capacity for empathic affect is advanced. More generally, the aspiration of the thesis is to provide an account of practical reasons framed in terms of the requirements of interpretable functioning which will be regarded as an interesting and credible naturalistic option.

The coneptual distinction between logic and control is an important tenet of logic programing. In practice, however, logic program languages use control strategies which profoundly affect the computational behavior of programs. For example, sequential Prolog's depth-first-left-first control is an unfair strategy under which nontermination can easily arise if programs are ill-structured. Formal analyses of logic programs therefore require an explicit formalisation of the control scheme. To this ends, this research introduces an algebraic proccess semantics of sequential logic programs written in Milner's calculus of Communicating Systems (CCS). the main contribution of this semantics is that the control component of a logic programming language is conciesly modelled. Goals and clauses of logic programs correspond semantically to sequential AND and OR agents respectively, and these agents are suitably defined to reflect the control strategy used to traverse the AND/OR computation tree for the program. The main difference between this and other process semantics which model concurrency is that the processes used here are sequential. The primary control strategy studied is standard Prolog's left-first-depth-first control. CCS is descriptively robust, however, and a variety of other sequential control schemes are modelled, including breadth-first, predicate freezing, and nondeterministic strategies. The CCS semantics for a particular control scheme is typically defined hierarchically. For example, standard Prolog control is initially defined in basic CCS using two control operators which model goal backtracking and clause sequencing. Using these basic definitions, higher-level bisimilarities are derived, ehich are more closely mappable to Prolog program constructs. By using variuos algebraic properties of the control operators, as well as the stream domain and theory of observational equivalence from CCS, a programming calculus approach to logic program analysis is permitted. Some example applications using the semantics include proving program termination, verifying transformations which use cut, and characterising some control issues of partial evaluation. Since progress algebras have already been used to model concurrency, this thesis suggests that they are an ideal means for unifying the operational semantics of the sequential and concurrent paradigms of logic programming.

<p> We created 4 sequences of chess moves intended (and verified) as sufficiently good (2 sequences), in play quality, or bad (2 sequences) to induce contrast. In experiment 1, 24 experienced chess-players (USCF Elo > 1300) watched these sequences and rated them with regards to overall quality (&minus;100 to +100) and estimated Elo ratings, a proxy for play quality, of the players involved. In experiment 2, a different group of 24 experienced chess-players rated the sequences of chess games by &ldquo;How much better did the winner play than the loser?&rdquo; on a 1 to 7 scale. Results revealed negative contrast (experiment 1) and no evidence of condensation (experiments 1 and 2) as well as the potential that one&rsquo;s own actual Elo may have anchored the ratings given to one set of stimuli.</p>

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This thesis examines two approaches to Galois correspondences in formal logic. A standard result of classical first-order model theory is the observation that models of L-theories with a weak form of elimination of imaginaries hold a correspondence between their substructures and automorphism groups defined on them. This work applies the resultant framework to explore the practical consequences of a model-theoretic Galois theory with respect to certain first-order L-theories. The framework is also used to motivate an examination of its underlying model-theoretic foundations. The model-theoretic Galois theory of pure fields and valued fields is compared to the algebraic Galois theory of pure and valued fields to point out differences that may hold between them. The framework of this logical Galois correspondence is also applied to the theory of pseudoexponentiation to obtain a sketch of the Galois theory of exponential fields, where the fixed substructure of the complex pseudoexponential field B is an exponential field with the field Qrab as its algebraic subfield. This work obtains a partial exponential analogue to the Kronecker-Weber theorem by describing the pure field-theoretic abelian extensions of Qrab, expanding upon work in the twelfth of Hilbert’s problems. This result is then used to determine some of the model-theoretic abelian extensions of the fixed substructure of B. This work also incorporates the principles required of this model-theoretic framework in order to develop a model theory over substructural logics which is capable of expressing this Galois correspondence. A formal semantics is developed for quantified predicate substructural logics based on algebraic models for their propositional or nonquantified fragments. This semantics is then used to develop substructural forms of standard results in classical first-order model theory. This work then uses this substructural model theory to demonstrate the Galois correspondence that substructural first-order theories can carry in certain situations.

No description available.