5,421 research outputs found
Introducing Quantified Cuts in Logic with Equality
Cut-introduction is a technique for structuring and compressing formal
proofs. In this paper we generalize our cut-introduction method for the
introduction of quantified lemmas of the form (for
quantifier-free ) to a method generating lemmas of the form . Moreover, we extend the original method to predicate
logic with equality. The new method was implemented and applied to the TSTP
proof database. It is shown that the extension of the method to handle equality
and quantifier-blocks leads to a substantial improvement of the old algorithm
Recommended from our members
Emotional Biosensing: Exploring Critical Alternatives
Emotional biosensing is rising in daily life: Data and categories claim to know how people feel and suggest what they should do about it, while CSCW explores new biosensing possibilities. Prevalent approaches to emotional biosensing are too limited, focusing on the individual, optimization, and normative categorization. Conceptual shifts can help explore alternatives: toward materiality, from representation toward performativity, inter-action to intra-action, shifting biopolitics, and shifting affect/desire. We contribute (1) synthesizing wide-ranging conceptual lenses, providing analysis connecting them to emotional biosensing design, (2) analyzing selected design exemplars to apply these lenses to design research, and (3) offering our own recommendations for designers and design researchers. In particular we suggest humility in knowledge claims with emotional biosensing, prioritizing care and affirmation over self- improvement, and exploring alternative desires. We call for critically questioning and generatively re- imagining the role of data in configuring sensing, feeling, ‘the good life,’ and everyday experience
On the Herbrand content of LK
We present a structural representation of the Herbrand content of LK-proofs
with cuts of complexity prenex Sigma-2/Pi-2. The representation takes the form
of a typed non-deterministic tree grammar of order 2 which generates a finite
language of first-order terms that appear in the Herbrand expansions obtained
through cut-elimination. In particular, for every Gentzen-style reduction
between LK-proofs we study the induced grammars and classify the cases in which
language equality and inclusion hold.Comment: In Proceedings CL&C 2016, arXiv:1606.0582
Elimination of Cuts in First-order Finite-valued Logics
A uniform construction for sequent calculi for finite-valued first-order logics with distribution quantifiers is exhibited. Completeness, cut-elimination and midsequent theorems are established. As an application, an analog of Herbrand’s theorem for the four-valued knowledge-representation logic of Belnap and Ginsberg is presented. It is indicated how this theorem can be used for reasoning about knowledge bases with incomplete and inconsistent information
Applying machine learning to the problem of choosing a heuristic to select the variable ordering for cylindrical algebraic decomposition
Cylindrical algebraic decomposition(CAD) is a key tool in computational
algebraic geometry, particularly for quantifier elimination over real-closed
fields. When using CAD, there is often a choice for the ordering placed on the
variables. This can be important, with some problems infeasible with one
variable ordering but easy with another. Machine learning is the process of
fitting a computer model to a complex function based on properties learned from
measured data. In this paper we use machine learning (specifically a support
vector machine) to select between heuristics for choosing a variable ordering,
outperforming each of the separate heuristics.Comment: 16 page
- …