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Toward a general theory of names
2005
Proceedings of the 3rd ACM SIGPLAN workshop on Mechanized reasoning about languages with variable binding - MERLIN '05
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In these cases, it appears necessary to either rearrange the abstract syntax so that lexical scoping can be used, or revert to first-order techniques. ...
Examples include binding transitions in the π-calculus; unique identifiers in contexts, memory heaps, and XML documents; declaration scoping in modules and namespaces; anonymous identifiers in automata ...
(an extension of first-order logic with a theory of names, binding, freshness, α-equivalence, and quantification over fresh names). ...
doi:10.1145/1088454.1088459
dblp:conf/icfp/Cheney05a
fatcat:i2aqd64ejvhpjpd6cec7af6jim
Mechanized meta-reasoning using a hybrid HOAS/de bruijn representation and reflection
2006
SIGPLAN notices
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In order to provide a standard, uniform account of a programming language, we propose to define it as a logic in a logical framework, using the same mechanisms for definition, reasoning, and automation ...
The principal representation used by the reflected logic is higher-order abstract syntax (HOAS). However, reasoning about terms in HOAS can be awkward in some cases, especially for variables. ...
In addition, for simple proofs, the first-order forms are entirely hidden. ...
doi:10.1145/1160074.1159826
fatcat:7cuns37lpfcshhshbglxocmeha
Mechanized meta-reasoning using a hybrid HOAS/de bruijn representation and reflection
2006
Proceedings of the eleventh ACM SIGPLAN international conference on Functional programming - ICFP '06
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In order to provide a standard, uniform account of a programming language, we propose to define it as a logic in a logical framework, using the same mechanisms for definition, reasoning, and automation ...
The principal representation used by the reflected logic is higher-order abstract syntax (HOAS). However, reasoning about terms in HOAS can be awkward in some cases, especially for variables. ...
In addition, for simple proofs, the first-order forms are entirely hidden. ...
doi:10.1145/1159803.1159826
dblp:conf/icfp/HickeyNYK06
fatcat:sg2yylhtibh6variv7navozsp4
Computational Limitations of First-Order Repressor Systems
[article]
2016
arXiv
pre-print
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Almost all current approaches for engineering modular logic components in synthetic biology use first-order regulators, including most CRISPR/CAS, TAL, zinc finger, and RNA interference systems. ...
first-order repressors. ...
The fused proteins form a homodimer and bind a palindromic sequence, resulting in second order binding. ...
arXiv:1608.03047v1
fatcat:zh6mrcwir5bq3p3m5glvpbe2ru
Binding modalities
2013
Journal of Logic and Computation
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We introduce the first-order logic FOS4 * in which modalities can bind individual variables and, in particular, can directly represent both de re and de dicto modalities. ...
The standard first-order reading of modality does not bind individual variables, i.e., if x is free in F (x), then x remains free in 2F (x). ...
In Section 2, we introduce the logic FOS4 * which is a version of first-order modal logic S4 2 in the richer language with binding modalities. ...
doi:10.1093/logcom/ext017
fatcat:tvm4izts2vbfnmz3bhd6ocm2ji
Programming with Higher-Order Logic, by Dale Miller and Gopalan Nadathur, Cambridge University Press, 2012, Hardcover, ISBN-10:052187940X, xiv + 306 pp
2014
Theory and Practice of Logic Programming
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This book is concerned with the second form when the underlying logic is higher-order logic. ...
Some of the most beautiful discoveries in programming languages are their tight connections to logic and proof theory. These connections take two basic forms. ...
Other uses of higherorder features can be accomplished in first-order languages, such as Prolog, by exploiting a form of reflection on syntax, but at the great cost of being extra-logical and therefore ...
doi:10.1017/s1471068414000027
fatcat:fh5pyehajzazjm6ynvgvc6ojlq
Substructural Operational Semantics as Ordered Logic Programming
2009
2009 24th Annual IEEE Symposium on Logic In Computer Science
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We describe a substructural logic with ordered, linear, and persistent propositions and then endow a fragment with a committed choice forward-chaining operational interpretation. ...
Exploiting higher-order terms in this metalanguage, we specify the operational semantics of a number of object language features, such as call-by-value, call-by-name, call-by-need, mutable store, parallelism ...
We would like to thank the anonymous reviewers for their comments, Jason Reed for a key insight in the proof of completeness, and Noam Zeilberger for pointing us to Laurent's unpublished note [9] . ...
doi:10.1109/lics.2009.8
dblp:conf/lics/PfenningS09
fatcat:4ou76lgejzazleihm2zqh7rzea
Logic Column 14: Nominal Logic and Abstract Syntax
[article]
2005
arXiv
pre-print
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Formalizing syntactic proofs of properties of logics, programming languages, security protocols, and other formal systems is a significant challenge, in large part because of the obligation to handle name-binding ...
After an overview of other approaches, we describe nominal abstract syntax and nominal logic, a logic for reasoning about nominal abstract syntax. ...
Nominal logic proper consists of first-order logic extended with a first-order axiomatization of swapping, freshness, and abstraction, and with a new form of quantified formula, Na.ϕ. ...
arXiv:cs/0511025v1
fatcat:sro6jwwv65f2jnmxlzsulzr7r4
On the Completeness of First-Order Knowledge Compilation for Lifted Probabilistic Inference
2011
Neural Information Processing Systems
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We then show how to obtain a completeness result using a first-order knowledge compilation approach for theories of formulae containing up to two logical variables. ...
To solve this problem, various lifted inference algorithms have been proposed that reason at the first-order level, about groups of objects as a whole. ...
Background We will use standard concepts of function-free first-order logic (FOL). ...
dblp:conf/nips/Broeck11
fatcat:mf6ue5mwcnddjit2qv5ul364zu
Logic Column 16: Higher-Order Abstract Syntax: Setting the Record Straight
[article]
2006
arXiv
pre-print
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This article responds to a critique of higher-order abstract syntax appearing in Logic Column 14, "Nominal Logic and Abstract Syntax", cs.LO/0511025. ...
Both HOAS and nominal logic provide a sophisticated treatment of binding structure not enjoyed by first-order accounts, but ones of very different character. ...
The fact that alpha-equivalence is built-in is a strength of HOAS (and of de Bruijn representation) not enjoyed by first-order abstract syntax or by nominal logic. ...
arXiv:cs/0607141v1
fatcat:dnqne3ezm5azzh366ud2ponn5a
A Deterministic Operational Semantics for Functional Logic Programs
2002
APPIA-GULP-PRODE Joint Conference on Declarative Programming
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Starting from a "big-step" semantics in natural style which relates expressions and their evaluated results-but it is not sufficient to cover concurrency, search strategies, or to reason about costs associated ...
to particular computations-, we define a "small-step" operational semantics which actually covers the advanced features of modern functional logic languages. ...
Similarly, the (first-order) semantics for lazy functional logic programs is described in two separated phases. ...
dblp:conf/agp/AlbertHH0V02
fatcat:ibspqattzbdbhpzugqsctehm64
Practical Reflection for Sequent Logics
2007
Electronical Notes in Theoretical Computer Science
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form a proof of 2 L T . ...
That is, to develop an account of system L and its meta-properties, one first defines the system L as a primitive logic, using the exact same syntax and definition mechanism that are used in not-reflective ...
For a quantifier of the form ∃X : Context{i}. · · · the variable X is a first-order variable in the meta-logic M CTT . ...
doi:10.1016/j.entcs.2007.01.019
fatcat:mgjmyggxzndmzlz4h2miffcx2q
Page 221 of Computational Linguistics Vol. 16, Issue 4
[page]
1990
Computational Linguistics
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The store is a list of quantifiers that bind the free variables in the logical form of the phrase. ...
Our treatment of quantifier storage is different from Cooper’s in two ways. First, Cooper’s grammar maps phrases to model-theoretic denotations, not logical forms. ...
Polyadic Quantification via Denoting Concepts
2010
Notre Dame Journal of Formal Logic
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It is shown that, appearances to the contrary notwithstanding, the background ontology of the earlier theory of denoting enables the full-blown expressive power of first-order polyadic quantification theory ...
The case provides an especially vivid illustration of the general point that structural (or ideological) austerity can be paid for in the coin of ontological extravagance. ...
First, while the order of the quantifiers in (a) and (b) is the same, the order of the binding occurrences of the variables is different. 2 Second, while the order of the quantifiers in (a) and (c) is ...
doi:10.1215/00294527-2010-023
fatcat:vkzm5lp3hzcv3eroeckmbq2i6a
Page 205 of Computational Linguistics Vol. 29, Issue 2
[page]
2003
Computational Linguistics
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So, although we are faced with the limitations for reasoning with first-order logic (validity is undecidable in first-order logic, and model generation is restricted to finite models), these limitations ...
The theorem-proving agent is used to find a counterproof for the DRS translated into first-order logic. The model-building agent is used to check whether the same DRS is satisfiable. ...
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