Motivated Action Theory: A Formal Theory of Causal Reasoning

When we reason about change over time, causation provides an implicit preference: we prefer sequences of situations in which one situation leads causally to the next, rather than sequences in which one situation follows another at random and without causal connections. In this paper, we explore the problem of temporal reasoning --- reasoning about change over time --- and the crucial role that causation plays in our intuitions. We examine previous approaches to temporal reasoning, and their shortcomings, in light of this analysis. We propose a new system for causal reasoning, motivated action theory, which builds upon causation as a crucial preference creterion. Motivated action theory solves the traditional problems of both forward and backward reasoning, and additionally provides a basis for a new theory of explanation.

Type-alpha DPLs

This paper introduces Denotational Proof Languages (DPLs). DPLs are languages for presenting, discovering, and checking formal proofs. In particular, in this paper we discus type-alpha DPLs---a simple class of DPLs for which termination is guaranteed and proof checking can be performed in time linear in the size of the proof. Type-alpha DPLs allow for lucid proof presentation and for efficient proof checking, but not for proof search. Type-omega DPLs allow for search as well as simple presentation and checking, but termination is no longer guaranteed and proof checking may diverge. We do not study type-omega DPLs here. We start by listing some common characteristics of DPLs. We then illustrate with a particularly simple example: a toy type-alpha DPL called PAR, for deducing parities. We present the abstract syntax of PAR, followed by two different kinds of formal semantics: evaluation and denotational. We then relate the two semantics and show how proof checking becomes tantamount to evaluation. We proceed to develop the proof theory of PAR, formulating and studying certain key notions such as observational equivalence that pervade all DPLs. We then present NDL, a type-alpha DPL for classical zero-order natural deduction. Our presentation of NDL mirrors that of PAR, showing how every basic concept that was introduced in PAR resurfaces in NDL. We present sample proofs of several well-known tautologies of propositional logic that demonstrate our thesis that DPL proofs are readable, writable, and concise. Next we contrast DPLs to typed logics based on the Curry-Howard isomorphism, and discuss the distinction between pure and augmented DPLs. Finally we consider the issue of implementing DPLs, presenting an implementation of PAR in SML and one in Athena, and end with some concluding remarks.

Type-omega DPLs

Type-omega DPLs (Denotational Proof Languages) are languages for proof presentation and search that offer strong soundness guarantees. LCF-type systems such as HOL offer similar guarantees, but their soundness relies heavily on static type systems. By contrast, DPLs ensure soundness dynamically, through their evaluation semantics; no type system is necessary. This is possible owing to a novel two-tier syntax that separates deductions from computations, and to the abstraction of assumption bases, which is factored into the semantics of the language and allows for sound evaluation. Every type-omega DPL properly contains a type-alpha DPL, which can be used to present proofs in a lucid and detailed form, exclusively in terms of primitive inference rules. Derived inference rules are expressed as user-defined methods, which are "proof recipes" that take arguments and dynamically perform appropriate deductions. Methods arise naturally via parametric abstraction over type-alpha proofs. In that light, the evaluation of a method call can be viewed as a computation that carries out a type-alpha deduction. The type-alpha proof "unwound" by such a method call is called the "certificate" of the call. Certificates can be checked by exceptionally simple type-alpha interpreters, and thus they are useful whenever we wish to minimize our trusted base. Methods are statically closed over lexical environments, but dynamically scoped over assumption bases. They can take other methods as arguments, they can iterate, and they can branch conditionally. These capabilities, in tandem with the bifurcated syntax of type-omega DPLs and their dynamic assumption-base semantics, allow the user to define methods in a style that is disciplined enough to ensure soundness yet fluid enough to permit succinct and perspicuous expression of arbitrarily sophisticated derived inference rules. We demonstrate every major feature of type-omega DPLs by defining and studying NDL-omega, a higher-order, lexically scoped, call-by-value type-omega DPL for classical zero-order natural deduction---a simple choice that allows us to focus on type-omega syntax and semantics rather than on the subtleties of the underlying logic. We start by illustrating how type-alpha DPLs naturally lead to type-omega DPLs by way of abstraction; present the formal syntax and semantics of NDL-omega; prove several results about it, including soundness; give numerous examples of methods; point out connections to the lambda-phi calculus, a very general framework for type-omega DPLs; introduce a notion of computational and deductive cost; define several instrumented interpreters for computing such costs and for generating certificates; explore the use of type-omega DPLs as general programming languages; show that DPLs do not have to be type-less by formulating a static Hindley-Milner polymorphic type system for NDL-omega; discuss some idiosyncrasies of type-omega DPLs such as the potential divergence of proof checking; and compare type-omega DPLs to other approaches to proof presentation and discovery. Finally, a complete implementation of NDL-omega in SML-NJ is given for users who want to run the examples and experiment with the language.

Formal Multilevel Hierarchical Verification of Synchronous MOS Circuits

I have designed and implemented a system for the multilevel verification of synchronous MOS VLSI circuits. The system, called Silica Pithecus, accepts the schematic of an MOS circuit and a specification of the circuit's intended digital behavior. Silica Pithecus determines if the circuit meets its specification. If the circuit fails to meet its specification Silica Pithecus returns to the designer the reason for the failure. Unlike earlier verifiers which modelled primitives (e.g., transistors) as unidirectional digital devices, Silica Pithecus models primitives more realistically. Transistors are modelled as bidirectional devices of varying resistances, and nodes are modelled as capacitors. Silica Pithecus operates hierarchically, interactively, and incrementally. Major contributions of this research include a formal understanding of the relationship between different behavioral descriptions (e.g., signal, boolean, and arithmetic descriptions) of the same device, and a formalization of the relationship between the structure, behavior, and context of device. Given these formal structures my methods find sufficient conditions on the inputs of circuits which guarantee the correct operation of the circuit in the desired descriptive domain. These methods are algorithmic and complete. They also handle complex phenomena such as races and charge sharing. Informal notions such as races and hazards are shown to be derivable from the correctness conditions used by my methods.

Asymptotically Zero Energy Computing Using Split-Level Charge Recovery Logic

The dynamic power requirement of CMOS circuits is rapidly becoming a major concern in the design of personal information systems and large computers. In this work we present a number of new CMOS logic families, Charge Recovery Logic (CRL) as well as the much improved Split-Level Charge Recovery Logic (SCRL), within which the transfer of charge between the nodes occurs quasistatically. Operating quasistatically, these logic families have an energy dissipation that drops linearly with operating frequency, i.e., their power consumption drops quadratically with operating frequency as opposed to the linear drop of conventional CMOS. The circuit techniques in these new families rely on constructing an explicitly reversible pipelined logic gate, where the information necessary to recover the energy used to compute a value is provided by computing its logical inverse. Information necessary to uncompute the inverse is available from the subsequent inverse logic stage. We demonstrate the low energy operation of SCRL by presenting the results from the testing of the first fully quasistatic 8 x 8 multiplier chip (SCRL-1) employing SCRL circuit techniques.

Reasoning about Temporal Context using Ontology and Abductive Constraint Logic Programming

The underlying assumptions for interpreting the meaning of data often change over time, which further complicates the problem of semantic heterogeneities among autonomous data sources. As an extension to the COntext INterchange (COIN) framework, this paper introduces the notion of temporal context as a formalization of the problem. We represent temporal context as a multi-valued method in F-Logic; however, only one value is valid at any point in time, the determination of which is constrained by temporal relations. This representation is then mapped to an abductive constraint logic programming framework with temporal relations being treated as constraints. A mediation engine that implements the framework automatically detects and reconciles semantic differences at different times. We articulate that this extended COIN framework is suitable for reasoning on the Semantic Web.

Reasoning about Temporal Context using Ontology and Abductive Constraint Logic Programming

The underlying assumptions for interpreting the meaning of data often change over time, which further complicates the problem of semantic heterogeneities among autonomous data sources. As an extension to the COntext INterchange (COIN) framework, this paper introduces the notion of temporal context as a formalization of the problem. We represent temporal context as a multi-valued method in F-Logic; however, only one value is valid at any point in time, the determination of which is constrained by temporal relations. This representation is then mapped to an abductive constraint logic programming framework with temporal relations being treated as constraints. A mediation engine that implements the framework automatically detects and reconciles semantic differences at different times. We articulate that this extended COIN framework is suitable for reasoning on the Semantic Web.

Reasoning about Temporal Context using Ontology and Abductive Constraint Logic Programming

The underlying assumptions for interpreting the meaning of data often change over time, which further complicates the problem of semantic heterogeneities among autonomous data sources. As an extension to the COntext INterchange (COIN) framework, this paper introduces the notion of temporal context as a formalization of the problem. We represent temporal context as a multi-valued method in F-Logic; however, only one value is valid at any point in time, the determination of which is constrained by temporal relations. This representation is then mapped to an abductive constraint logic programming framework with temporal relations being treated as constraints. A mediation engine that implements the framework automatically detects and reconciles semantic differences at different times. We articulate that this extended COIN framework is suitable for reasoning on the Semantic Web.

Reasoning about Temporal Context using Ontology and Abductive Constraint Logic Programming

The underlying assumptions for interpreting the meaning of data often change over time, which further complicates the problem of semantic heterogeneities among autonomous data sources. As an extension to the COntext INterchange (COIN) framework, this paper introduces the notion of temporal context as a formalization of the problem. We represent temporal context as a multi-valued method in F-Logic; however, only one value is valid at any point in time, the determination of which is constrained by temporal relations. This representation is then mapped to an abductive constraint logic programming framework with temporal relations being treated as constraints. A mediation engine that implements the framework automatically detects and reconciles semantic differences at different times. We articulate that this extended COIN framework is suitable for reasoning on the Semantic Web.