Natural deduction as higher-order resolution
Journal of Logic Programming
PLDI '88 Proceedings of the ACM SIGPLAN 1988 conference on Programming Language design and Implementation
A finitary version of the calculus of partial inductive definitions
ELP'91 Conference Proceedings on Extensions of logic programming
Unification under a mixed prefix
Journal of Symbolic Computation
Modal logics for mobile processes
Selected papers of the 3rd workshop on Concurrency and compositionality
A calculus of mobile processes, II
Information and Computation
MFPS '92 Selected papers of the meeting on Mathematical foundations of programming semantics
A theory of bisimulation for the &lgr;-calculus
Acta Informatica
A symbolic semantics for the &pgr;-calculus
Information and Computation
Cut-elimination for a logic with definitions and induction
Theoretical Computer Science - Special issue on proof-search in type-theoretic languages
Foundational aspects of syntax
ACM Computing Surveys (CSUR)
&pgr;-calculus in (Co)inductive-type theory
Theoretical Computer Science - Special issues on models and paradigms for concurrency
Reasoning with higher-order abstract syntax in a logical framework
ACM Transactions on Computational Logic (TOCL)
PI-Calculus: A Theory of Mobile Processes
PI-Calculus: A Theory of Mobile Processes
Local and Symbolic Bisimulation Using Tabled Constraint Logic Programming
Proceedings of the 17th International Conference on Logic Programming
Final semantics for the pi-calculus
PROCOMET '98 Proceedings of the IFIP TC2/WG2.2,2.3 International Conference on Programming Concepts and Methods
A Full Formalisation of pi-Calculus Theory in the Calculus of Constructions
TPHOLs '97 Proceedings of the 10th International Conference on Theorem Proving in Higher Order Logics
Encoding transition systems in sequent calculus
Theoretical Computer Science - Linear logic
A Proof Theory for Generic Judgments: An extended abstract
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
Nominal logic, a first order theory of names and binding
Information and Computation - TACS 2001
Some uses of higher-order logic in computational linguistics
ACL '86 Proceedings of the 24th annual meeting on Association for Computational Linguistics
A logical framework for reasoning about logical specifications
A logical framework for reasoning about logical specifications
A treatment of higher-order features in logic programming
Theory and Practice of Logic Programming
A proof theory for generic judgments
ACM Transactions on Computational Logic (TOCL)
Model checking for π-calculus using proof search
CONCUR 2005 - Concurrency Theory
A Proof Search Specification of the π-Calculus
Electronic Notes in Theoretical Computer Science (ENTCS)
A Congruence Format for Name-passing Calculi
Electronic Notes in Theoretical Computer Science (ENTCS)
Formalising the π-calculus using nominal logic
FOSSACS'07 Proceedings of the 10th international conference on Foundations of software science and computational structures
Least and greatest fixed points in linear logic
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
Practical higher-order pattern unification with on-the-fly raising
ICLP'05 Proceedings of the 21st international conference on Logic Programming
Nominal techniques in Isabelle/HOL
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
Focusing and polarization in intuitionistic logic
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
Information and Computation
Reasoning about computations using two-levels of logic
APLAS'10 Proceedings of the 8th Asian conference on Programming languages and systems
A supposedly fun thing i may have to do again: a HOAS encoding of Howe's method
Proceedings of the seventh international workshop on Logical frameworks and meta-languages, theory and practice
Proof pearl: abella formalization of λ-calculus cube property
CPP'12 Proceedings of the Second international conference on Certified Programs and Proofs
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We specify the operational semantics and bisimulation relations for the finite π-calculus within a logic that contains the ∇ quantifier for encoding generic judgments and definitions for encoding fixed points. Since we restrict to the finite case, the ability of the logic to unfold fixed points allows this logic to be complete for both the inductive nature of operational semantics and the coinductive nature of bisimulation. The ∇ quantifier helps with the delicate issues surrounding the scope of variables within π-calculus expressions and their executions (proofs). We illustrate several merits of the logical specifications permitted by this logic: they are natural and declarative; they contain no side-conditions concerning names of variables while maintaining a completely formal treatment of such variables; differences between late and open bisimulation relations arise from familar logic distinctions; the interplay between the three quantifiers (∀, &exists;, and ∇) and their scopes can explain the differences between early and late bisimulation and between various modal operators based on bound input and output actions; and proof search involving the application of inference rules, unification, and backtracking can provide complete proof systems for one-step transitions, bisimulation, and satisfaction in modal logic. We also illustrate how one can encode the π-calculus with replications, in an extended logic with induction and co-induction.