Related papers: Schematic Polymorphism in the Abella Proof Assista…
Abella is an interactive system for reasoning about aspects of object languages that have been formally presented through recursive rules based on syntactic structure. Abella utilizes a two-level logic approach to specification and…
The approach to reasoning about structural operational semantics style specifications supported by the Abella system is discussed. This approach uses lambda tree syntax to treat object language binding and encodes binding related properties…
Relational descriptions have been used in formalizing diverse computational notions, including, for example, operational semantics, typing, and acceptance by non-deterministic machines. We therefore propose a (restricted) logical theory…
Treating syntactic equality as a logical connective -- governed by left- and right-introduction rules within the sequent calculus -- offers an elegant and powerful approach to term identity. This treatment of equality allows for the…
This thesis concerns the development of a framework that facilitates the design and analysis of formal systems. Specifically, this framework provides a specification language which supports the concise and direct description of formal…
In logical reasoning, it is often the case that only some of a collection of assumptions are needed to reach a conclusion. A strengthening lemma is an assertion that a given conclusion is independent in this sense of a particular…
When reasoning about formal objects whose structures involve binding, it is often necessary to analyze expressions relative to a context that associates types, values, and other related attributes with variables that appear free in the…
This thesis develops a framework for formalizing reasoning about specifications of systems written in LF. This formalization centers around the development of a reasoning logic that can express the sorts of properties which arise in…
Structural proof theory is praised for being a symbolic approach to reasoning and proofs, in which one can define schemas for reasoning steps and manipulate proofs as a mathematical structure. For this to be possible, proof systems must be…
Simple type theory is formulated for use with the generic theorem prover Isabelle. This requires explicit type inference rules. There are function, product, and subset types, which may be empty. Descriptions (the eta-operator) introduce the…
The logic underlying the Abella proof assistant includes mechanisms for interpreting atomic predicates through fixed point definitions that can additionally be treated inductively or co-inductively. However, the original formulation of the…
The logic of hereditary Harrop formulas (HH) has proven useful for specifying a wide range of formal systems. This logic includes a form of hypothetical judgment that leads to dynamically changing sets of assumptions and that is key to…
The logic of definitions is a family of logics for encoding and reasoning about judgments, which are atomic predicates specified by inference rules. A definition associates an atomic predicate with a logical formula, which may itself depend…
Isabelle is a generic theorem prover, designed for interactive reasoning in a variety of formal theories. At present it provides useful proof procedures for Constructive Type Theory, various first-order logics, Zermelo-Fraenkel set theory,…
Isabelle is an interactive theorem prover that supports a variety of logics. It represents rules as propositions (not as functions) and builds proofs by combining rules. These operations constitute a meta-logic (or `logical framework') in…
A logic is presented for reasoning on iterated sequences of formulae over some given base language. The considered sequences, or "schemata", are defined inductively, on some algebraic structure (for instance the natural numbers, the lists,…
The dependently-typed lambda calculus LF is often used as a vehicle for formalizing rule-based descriptions of object systems. Proving properties of object systems encoded in this fashion requires reasoning about formulas over LF typing…
Isabelle is a generic theorem prover with a fragment of higher-order logic as a metalogic for defining object logics. Isabelle also provides proof terms. We formalize this metalogic and the language of proof terms in Isabelle/HOL, define an…
Large language models (LLMs) have shown promise in table Question Answering (Table QA). However, extending these capabilities to multi-table QA remains challenging due to unreliable schema linking across complex tables. Existing methods…
Many problems can be specified by patterns of propositional formulae depending on a parameter, e.g. the specification of a circuit usually depends on the number of bits of its input. We define a logic whose formulae, called "iterated…