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Deciding Monodic Fragments by Temporal Resolution [chapter]

Ullrich Hustadt, Boris Konev, Renate A. Schmidt
2005 Lecture Notes in Computer Science  
In this paper we study the decidability of various fragments of monodic first-order temporal logic by temporal resolution.  ...  This allows us to transfer existing results on decidability by resolution for first-order fragments to monodic first-order temporal logic and obtain new decision procedures.  ...  Theorem 3 (Decidability by Temporal Resolution).  ... 
doi:10.1007/11532231_15 fatcat:wc3jt23qkvctffj3juroxe2unu

Handling Equality in Monodic Temporal Resolution [chapter]

Boris Konev, Anatoli Degtyarev, Michael Fisher
2003 Lecture Notes in Computer Science  
While the full logic is highly complex, recent work on monodic first-order temporal logics has identified important enumerable and even decidable fragments including the guarded fragment with equality.  ...  In this paper, we specialise the monodic resolution method to the guarded monodic fragment with equality and first-order temporal logic over expanding domains.  ...  Satisfiability of the guarded monodic temporal fragment with equality is decidable by temporal resolution.  ... 
doi:10.1007/978-3-540-39813-4_15 fatcat:w76ceqmpjzbr7ahfhr4tlevwlq

Monodic ASMs and Temporal Verification [chapter]

Michael Fisher, Alexei Lisitsa
2004 Lecture Notes in Computer Science  
This, together with recent work on clausal resolution methods for monodic fragments, allows us to carry out temporal verification of monodic ASMs.  ...  Thus, in this paper, we define a class of monodic ASMs whose semantics in terms of temporal logic fits within the monodic fragment.  ...  translation is in a 'good' (monodic) fragment of FOTL.  ... 
doi:10.1007/978-3-540-24773-9_8 fatcat:qhkxpto2b5azjkyl44anuxyz3i

Monodic temporal resolution [article]

Anatoly Degtyarev, Michael Fisher, Boris Konev
2003 arXiv   pre-print
These include definitions of new decidable monodic classes, simplification of existing monodic classes by reductions, and completeness of clausal temporal resolution in the case of monodic logics with  ...  In this paper, we modify and extend the clausal temporal resolution technique, originally developed for propositional temporal logics, to enable its use in such monodic fragments.  ...  [18] showed that monodic fragments of FOTL could be complete, even decidable.  ... 
arXiv:cs/0306041v1 fatcat:7sid7xebkfg5radngfdawnuoui

Monodic temporal resolution

Anatoli Degtyarev, Michael Fisher, Boris Konev
2006 ACM Transactions on Computational Logic  
[Hodkinson et al. 2000] showed that monodic fragments of ÇÌÄ could be complete, even decidable.  ...  Although a tableaux based approach was proposed in [Kontchakov et al. 2004] , we here provide a complete resolution calculus for monodic  ...  The third author is supported in part by Award No. RM1-2409-ST-02 of the U.S. Civilian Research & Development Foundation for the Independent States of the Former Soviet Union (CRDF).  ... 
doi:10.1145/1119439.1119443 fatcat:3gecwo5uk5halc33ey5uf4kqcu

Monodic Temporal Resolution [chapter]

Anatoly Degtyarev, Michael Fisher, Boris Konev
2003 Lecture Notes in Computer Science  
[Hodkinson et al. 2000] showed that monodic fragments of ÇÌÄ could be complete, even decidable.  ...  Although a tableaux based approach was proposed in [Kontchakov et al. 2004] , we here provide a complete resolution calculus for monodic  ...  The third author is supported in part by Award No. RM1-2409-ST-02 of the U.S. Civilian Research & Development Foundation for the Independent States of the Former Soviet Union (CRDF).  ... 
doi:10.1007/978-3-540-45085-6_35 fatcat:nrhzv7ortza6lchpkgurtfnsuq

Mechanising first-order temporal resolution

Boris Konev, Anatoli Degtyarev, Clare Dixon, Michael Fisher, Ullrich Hustadt
2005 Information and Computation  
While the full logic is highly complex, recent work on monodic first-order temporal logics has identified important enumerable and even decidable fragments.  ...  By careful encoding, parts of the calculus can be implemented using classical first-order resolution and can, thus, be efficiently implemented.  ...  Moreover, the transformation maps formulae in the temporal logics of knowledge into a subclass of the monodic fragment which is decidable by temporal resolution (see Note 2) .  ... 
doi:10.1016/j.ic.2004.10.005 fatcat:uwush6mgpfhrbgw4nfgs3yehgu

Towards First-Order Temporal Resolution [chapter]

Anatoli Degtyarev, Michael Fisher
2001 Lecture Notes in Computer Science  
In this paper we show how to extend clausal temporal resolution to the ground eventuality fragment of monodic first-order temporal logic, which has recently been introduced by Hodkinson, Wolter and Zakharyaschev  ...  While a finite Hilbert-like axiomatization of complete monodic first order temporal logic was developed by Wolter and Zakharyaschev, we propose a temporal resolutionbased proof system which reduces the  ...  The monodic fragment is the only known today fragment of first-order temporal logic among not only decidable but even recursively enumerable fragments which has a transparent syntactical definition and  ... 
doi:10.1007/3-540-45422-5_3 fatcat:vdh74igymfe3xbd6lv5txdrery

A Survey on Temporal Logics [article]

Savas Konur
2011 arXiv   pre-print
This paper surveys main and recent studies on temporal logics in a broad sense by presenting various logic systems, dealing with various time structures, and discussing important features, such as decidability  ...  This work was partially supported by EPSRC research project EP/F033567.  ...  In [11, 69] monodic guarded decidable fragments are introduced by restricting the quantification.  ... 
arXiv:1005.3199v3 fatcat:nogsv2iggvd5likbkrnmnzpsdu

Temporal Verification of Fault-Tolerant Protocols [chapter]

Michael Fisher, Boris Konev, Alexei Lisitsa
2009 Lecture Notes in Computer Science  
logic [4, 23] ; and 4. deductive verification in first-order decidable temporal logics [12, 8] .  ...  Monodic First-Order Temporal Logics First-order (linear time) temporal logic (FOTL) is a very powerful and expressive formalism in which the specification of many algorithms, protocols and computational  ...  The monodic fragment of FOTL has appealing properties: it is axiomatisable [24] and many of its sub-fragments, such as the two-variable or monadic cases, are decidable.  ... 
doi:10.1007/978-3-642-00867-2_3 fatcat:tcdublimrzc7hjhix57heeywae

Fair Derivations in Monodic Temporal Reasoning [chapter]

Michel Ludwig, Ullrich Hustadt
2009 Lecture Notes in Computer Science  
In this paper we focus on ordered fine-grained resolution with selection, a sound and complete resolution-based calculus for monodic first-order temporal logic.  ...  The elimination of redundant clauses is an essential part of resolution-based theorem proving in order to reduce the size of the search space.  ...  Introduction Monodic first-order temporal logic [9] is a fragment of first-order temporal logic (without equality) which, in contrast to first-order temporal logic itself, has a semi-decidable validity  ... 
doi:10.1007/978-3-642-02959-2_21 fatcat:iiy2lyepvrcuzgqrbmxh6m2izy

Complexity of monodic guarded fragments over linear and real time

Ian Hodkinson
2006 Annals of Pure and Applied Logic  
We show that the satisfiability problem for the monodic guarded, loosely guarded, and packed fragments of first-order temporal logic with equality is 2Exptime-complete for structures with arbitrary first-order  ...  the natural numbers, integers, rationals, and any first-order definable class of linear flows of time. * Research partially supported by U.K.  ...  Recently, however, some decidable fragments of first-order temporal logic have been found. The so-called monodic fragments, originating in [15] , have now been quite extensively investigated.  ... 
doi:10.1016/j.apal.2005.06.007 fatcat:nw5xsjjfyffijmaaarbo3q3nuu

Searching for Invariants Using Temporal Resolution [chapter]

James Brotherston, Anatoli Degtyarev, Michael Fisher, Alexei Lisitsa
2002 Lecture Notes in Computer Science  
In this paper, we show how the clausal temporal resolution technique developed for temporal logic provides an effective method for searching for invariants, and so is suitable for mechanising a wide class  ...  In this paper, we show how the clausal temporal resolution technique developed for temporal logic provides an effective method for searching for invariants, and so is suitable for mechanising a wide class  ...  In [DF01] a clausal temporal resolution procedure has been developed covering a special subclass of the monodic fragment, namely the subclass of ground eventuality monodic problems.  ... 
doi:10.1007/3-540-36078-6_6 fatcat:inec3loxvndifmfmona2a2wd64

Practical First-Order Temporal Reasoning

Clare Dixon, Michael Fisher, Boris Konev, Alexei Lisitsa
2008 2008 15th International Symposium on Temporal Representation and Reasoning  
In this paper we consider the specification and verification of infinite-state systems using temporal logic.  ...  Importantly, the power of the temporal language allows us to describe (and verify) asynchronous systems, communication delays and more complex liveness and fairness properties.  ...  The resolution theorem-prover TeMP [21] provides a a practical approach to proving monodic temporal formulae.  ... 
doi:10.1109/time.2008.15 dblp:conf/time/DixonFKL08 fatcat:foba4kp24rbtpfl47iqocx4hxa

Efficient First-Order Temporal Logic for Infinite-State Systems [article]

Clare Dixon, Michael Fisher, Boris Konev, Alexei Lisitsa
2007 arXiv   pre-print
In this paper we consider the specification and verification of infinite-state systems using temporal logic.  ...  Importantly, the power of the temporal language allows us to describe (and verify) asynchronous systems, communication delays and more complex properties such as liveness and fairness properties.  ...  Proof methods for the monodic fragment of first order-temporal logics, based on resolution or tableaux have been proposed in [7, 26, 27] .  ... 
arXiv:cs/0702036v1 fatcat:esdkb3ltobgmtjxemha445r2iy
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