Morita Equivalence

Logicians and philosophers of science have proposed various formal criteria for theoretical equivalence. In this paper, we examine two such proposals: definitional equivalence and categorical equivalence. In order to show precisely how these two well-known criteria are related to one another, we investigate an intermediate criterion called Morita equivalence.Comment: 30 page

On finite imaginaries

We study finite imaginaries in certain valued fields, and prove a conjecture of Cluckers and Denef.Comment: 15p

Stable domination and independence in algebraically closed valued fields

We seek to create tools for a model-theoretic analysis of types in algebraically closed valued fields (ACVF). We give evidence to show that a notion of 'domination by stable part' plays a key role. In Part A, we develop a general theory of stably dominated types, showing they enjoy an excellent independence theory, as well as a theory of definable types and germs of definable functions. In Part B, we show that the general theory applies to ACVF. Over a sufficiently rich base, we show that every type is stably dominated over its image in the value group. For invariant types over any base, stable domination coincides with a natural notion of `orthogonality to the value group'. We also investigate other notions of independence, and show that they all agree, and are well-behaved, for stably dominated types. One of these is used to show that every type extends to an invariant type; definable types are dense. Much of this work requires the use of imaginary elements. We also show existence of prime models over reasonable bases, possibly including imaginaries

The Vampire and the FOOL

This paper presents new features recently implemented in the theorem prover Vampire, namely support for first-order logic with a first class boolean sort (FOOL) and polymorphic arrays. In addition to having a first class boolean sort, FOOL also contains if-then-else and let-in expressions. We argue that presented extensions facilitate reasoning-based program analysis, both by increasing the expressivity of first-order reasoners and by gains in efficiency

On Deciding Local Theory Extensions via E-matching

Satisfiability Modulo Theories (SMT) solvers incorporate decision procedures for theories of data types that commonly occur in software. This makes them important tools for automating verification problems. A limitation frequently encountered is that verification problems are often not fully expressible in the theories supported natively by the solvers. Many solvers allow the specification of application-specific theories as quantified axioms, but their handling is incomplete outside of narrow special cases. In this work, we show how SMT solvers can be used to obtain complete decision procedures for local theory extensions, an important class of theories that are decidable using finite instantiation of axioms. We present an algorithm that uses E-matching to generate instances incrementally during the search, significantly reducing the number of generated instances compared to eager instantiation strategies. We have used two SMT solvers to implement this algorithm and conducted an extensive experimental evaluation on benchmarks derived from verification conditions for heap-manipulating programs. We believe that our results are of interest to both the users of SMT solvers as well as their developers

Theory of Regulatory Compliance for Requirements Engineering

Regulatory compliance is increasingly being addressed in the practice of requirements engineering as a main stream concern. This paper points out a gap in the theoretical foundations of regulatory compliance, and presents a theory that states (i) what it means for requirements to be compliant, (ii) the compliance problem, i.e., the problem that the engineer should resolve in order to verify whether requirements are compliant, and (iii) testable hypotheses (predictions) about how compliance of requirements is verified. The theory is instantiated by presenting a requirements engineering framework that implements its principles, and is exemplified on a real-world case study.Comment: 16 page

Shapelessness in context

Many philosophers believe that the extensions of evaluative terms and concepts aren't unified under non-evaluative similarity relations and that this "shapelessness thesis" (ST) has significant metaethical implications regarding non-cognitivism, ethical naturalism, moral particularism, thick concepts and more. ST is typically offered as an explanation of why evaluative classifications appear to "outrun" classifications specifiable in independently intelligible non-evaluative terms. This paper argues that both ST and the outrunning point used to motivate it can be explained on the basis of more general factors that have nothing in particular to do with being evaluative. Insofar as ST is plausible, a wide variety of non-evaluative terms will also be such that the extension of a term T isn't unified under similarity relations specifiable in purely T-free terms. If so, there is no reason to expect ST to carry the sorts of metaethical implications that get attributed to it. I also show that my main argument is robust across certain complications that are raised by the context-sensitivity of many evaluative terms but have so far been ignored in discussions of ST and related matters